prove that.....cos^2α(cosec^2α-cot^2α)=cos^2α​

Answers

Answer 1

Step-by-step explanation:

We must prove that

cos²a(csc²a-cot²a) = cos²a

If we look at both sides, we can see that we have cos²a * something = cos²a. Therefore, if we can get that something to equal 1, we have our proof. In this case, that something is csc²a-cot²a. Using this information, we can work from within the parenthesis and go from there.

We can start by expanding the items in the parenthesis. Taking that csc(x) = 1/sin(x) and cot(a) = cos(x)/sin(x), we can say that

cos²a(csc²a-cot²a) = cos²a(1/sin²a - cos²a/sin²a). Because both items in the parenthesis have a denominator of sin²a, we can subtract cos²a from 1 to get

cos²a(1/sin²a - cos²a/sin²a)= cos²a((1-cos²a)/sin²a))

Next, we know that cos²a+sin²a=1, so 1-cos²a = sin²a. Plugging that in, we get

cos²a((1-cos²a)/sin²a)) = cos²a(sin²a/sin²a)

= cos²a(1)

= cos²a


Related Questions

Eric and Shiloh each have a savings account. The ratio of Eric’s account balance to Shiloh’s account balance is 4:3. Together they have a total of $140 in their accounts. Use the tape diagram below to help you determine the balance of Eric’s account. [Type your answer as a number.]

Answers

Answer:

Eric   80

Step-by-step explanation:

Take 4+3 = 7

140 /7 = 20

There is 20 in each block

Eric gets 4 of the blocks so 4*20 = 80

Shiloh gets 3 of the blocks 3*20 = 60

Answer:

80

Step-by-step explanation:

4 : 3

4x + 3x = 140

7x = 140

x =20

4*20 = eric's amount

= 80

If you don’t know the answer please don’t respond. I actually need help :)

Answers

Answer:

I don't know the answer to this question

I could really use some help

Answers

045 bearing the three figure for north east

Answer:

045

Step-by-step explanation:

North is equal to 360 or 0 degrees. East is equal to 90 degrees because that is 1/4 of 360.

Thus, northeast is 45 degrees. This image may help.

Select the expression that shows the distributive property applied to
13(2+9).
18 of 29 QUESTIONS
13(9+2)
13. 2+ 9
13. 2+ 13.9
13. 2+ 2.9

Answers

3rd option is correct

13 × 2 + 13 × 9

2. Peter wants to order tickets to a production of Charles Dickens' A Christmas Carol. Each ticket
costs $30 and there is a one time service fee of $12 for the transaction. What is an expression that
would find the total cost for any number of tickets that Peter orders? Use t for the variable to
represent the number of tickets he purchased.
Answer

Answers

Answer:

There is overwhelming evidence that human activities, especially burning fossil fuels, are leading to increased levels of carbon dioxide and other greenhouse gases in the atmosphere, which in turn amplify the natural greenhouse effect, causing the temperature of the Earth's atmosphere, ocean, and land surface to ...

solve the equation 4+2|3x+4|=-4

“Absolute Value Equations and Inequalities”
the solutions are what?

please give an explanation if possible!

Answers

Answer:

Value of given expression x is -4

Step-by-step explanation:

Given equation in question;

4 + 2|3x + 4| = -4

Find:

Value of given expression

Computation:

4 + 2|3x + 4| = -4

Using BODMAS rule;

⇒ 4 + 2|3x + 4| = -4

⇒ 2|3x + 4| = - 4 - 4

⇒ 2|3x + 4| = - 8

⇒ |3x + 4| = - 8 / 2

⇒ |3x + 4| = - 4

⇒ 3x + 4 = - 8

⇒ 3x = -8 - 4

⇒ 3x = -12

⇒ x = -12 / 3

⇒ x = -4

Value of given expression x is -4


Find the volume of a sphere with a diameter of 17.2 cm. Use 3.14 for it Round your answer to the nearest
tenth

Answers

Answer:

2663.0 cm³ (3 s.f.)

Step-by-step explanation:

[tex]\boxed{volume \: of \: sphere = \frac{4}{3}\pi {r}^{3} }[/tex]

Radius= diameter ÷2

Radius of sphere

= 17.2 ÷2

= 8.6 cm

Volume of sphere

[tex] = \frac{4}{3} (3.14)(8.6)^{3} [/tex]

= 2663.0 cm³ (3 s.f.)

How to change the decimal 4.5 into a fraction

Answers

4.5

= 4.5/1

= 4.5/1.0

= 45/10 [Shifting the decimal to right]

= 9/2 [Reducing to the simplest form]

So, the answer is 9/2.

5. Find the measures of the following. Round to the nearest whole number. (2 points)
a. HT
H
b. 2T
15 cm
C. ZH
W
8 cm
T

Answers

Answer:

HT = 17 cm

<T = 58°

<H = 32°

Step-by-step explanation:

✔️Find HT:

Since it's a right triangle, we would apply the Pythagorean Theorem given as c² = a² + b²

Where,

a = HW = 15 cm

b = WT = 8 cm

c = HT

Plug in the values:

HT² = 15² + 8²

HT² = 289

HT = √289

HT = 17 cm

✔️Find <T by applying trigonometric ratio formula:

Recall: SOH CAH TOA

Reference angle (θ) = <T

HW = 15 cm = Opposite side length

WT = 8 cm = Adjacent side length

Apply CAH:

Cos θ = Adj/Hyp

Substitute

Cos T = 8/15

T = [tex] cos^{-1}(0.5333) [/tex]

T ≈ 58°

✔️Find <H:

Sun of interior angles of a triangle = 180°

Therefore,

m<H + m<T + m<W = 180°

Substitute

m<H + 58° + 90° = 180°

m<H + 148° = 180°

m<H = 180° - 148°

m<H = 32°

Which set of ordered pairs does NOT represent a function?
{(0, 0), (1, 1), (2, 2), (3, 3)}
(0, 0), (0, 1), (1, 2), (1, 3)}
{(1,0), (2, 0), (3, 0), (4, 0)}
{(0, 1), (1, 2), (2, 3), (3, 4)}

Answers

Answer: (0, 0), (0, 1), (1, 2), (1, 3) does NOT represent a function

Step-by-step explanation:

to tell whether a set of ordered pairs are functions or not, all domains must have different ranges!

range: x-axis (0,0)

domain: y-axis (0,0)

pair 1:

all the ranges - 0, 1, 2, 3 - are different, which means it IS a set of ordered pairs

pair 2:

all the ranges - 0, 0, 1, 1 - are NOT all different, which means it is NOT a set of ordered pairs

pair 3:

all the ranges - 1, 2, 3, 4 - are different, which means it IS a set of ordered pairs

pair 4:

all the ranges - 0, 1, 2, 3 - are different, which means it IS a set of ordered pairs

let me know if you have any more questions or if i made any mistakes. hope this helped, and good luck! ˶ˆ꒳ˆ˵

Which of the following statements is false ?

Answers

Answer:

The bases of an isosceles trapezoid are congruent is false.

Step-by-step explanation:

Let's analyse each option.

In a Rhombus, the diagonals are perpendicular at the point of intersection and bisect each other is true.

In isosceles trapezoid, the sides are congruent but not the bases. So, this incorrect!

The rectangle is an Equi-angular because all the angles are equal. So, this is true.

The base angles are congruent in isosceles trapezoid. So, this is true too.

Help Please Now!!!
Find the volume of the rectangle prism

Answers

Answer:

V =48 cm^3

Step-by-step explanation:

The volume of a prism is given by

V = l*w*h

V = 3*4*4

V =48 cm^3

V =48 cm^3

Step-by-step explanation:

The volume of a prism is given by

V = l*w*h

V = 3*4*4

V =48 cm^3

Please help me anyone

Answers

Answer:

Step-by-step explanation:

y = x^2 + 4

x = 11  Put this value in wherever you see an x on the right.

y = 11^2 + 4

11^2 = 11 * 11 = 121

y = 121 + 4

y = 125


In the graph, what does A represent?
major axis
vertices
minor axis
foci

Answers

Minor axis because major is Y

An ellipse is a plane curve that surrounds two focus points and has a constant sum of the two distances to the focal points at all places on the curve. In the graph, the A represents the minor axis of the ellipse.

What is the equation of ellipse if its major and minor axis and center are given?

Suppose that the major axis is of the length 2a units, and that minor axis is of 2b units, and let the ellipse is centered on (h,k) with major ellipse parallel to x-axis, then the equation of that ellipse would be:

[tex]\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2} =1[/tex]

Coordinates of its foci would be: (h±c, k) where c² = a² - b²

If its major axis is parallel to y-axis, then,

coordinates of its foci would be:  (h, k±c) where c² = a² - b² and its equation would be:

[tex]\dfrac{(x-h)^2}{b^2} + \dfrac{(y-k)^2}{a^2} =1[/tex]

An ellipse is a plane curve that surrounds two focus points and has a constant sum of the two distances to the focal points at all places on the curve. Since an ellipse has two diameter, the major and the minor diameter. Therefore, in the graph, the A represents the minor axis of the ellipse.

Learn more about Ellipse here:

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SOLVE EQUATION
solve for x
|3x+19|=13

Answers

Answer:

answer is 20............

Step-by-step explanation:

3x=13-19

x= -6/3

x= -2

Answer:

= -2

Step-by-step explanation:

3x+19=13

3x=13-19

3x/3= 6/3

X= -2

Answer from Gauthmath

can i get some help? i tried figuring it out myself already but i must have done something wrong. please help!

Answers

First, we'll set up two equations. One for the amount of each coin and another for the value of the coins.

N will represent nickels

D will represent dimes

N + D = 30

---The problem tells us that there are 30 total coins

0.05N + 0.10D = 2.95

---Nickels are worth 5 cents and dimes are worth 10 cents, and the total value of the coins is 2.95

Now that we have our equations, we need to solve for one of the variables in the first equation. I will solve for N.

N + D = 30

N = 30 - D

Then, we take that equation and substitute our new value for N into the second equation (value) and solve for D.

0.05(30 - D) + 0.10D = 2.95

1.5 - 0.05D + 0.10D = 2.95

1.5 + 0.05D = 2.95

0.05D = 1.45

D = 29

Now that we know how many dimes there are, we can plug that value into our equation for N and solve for N.

N = 30 - D

N = 30 - 29

N = 1

Therefore, there are 29 dimes and 1 nickel.

Hope this helps!

A school is painting its logo in the shape of a triangle in the middle of its sports field. The school wants the height of the triangle to be 8 feet. The area of the logo must be at least 36 square feet. (The logo has to be seen from all the seats.) Write an inequality that describes the possible base lengths (in feet) of the triangle.
Use b for the base length of the triangular logo.

SOMEONE PLS HELP ME! THANK YOU!

Answers

Answer:

[tex]b\geq 9[/tex]

In other words, the base must be at least 9 feet long.

Step-by-step explanation:

The schools wants the height of the triangle to be eight feet, and the area of the logo to be at least 36 square feet.

Recall that the area of a triangle is given by:

[tex]\displaystyle A = \frac{1}{2}bh[/tex]

Since we want to area to be at least 36 square feet:

[tex]\displaystyle \frac{1}{2}bh \geq 36[/tex]

We are given that the height is eight feet. Substitute:

[tex]\displaystyle \frac{1}{2}(8)b\geq 36[/tex]

Simplify:

[tex]4b\geq 36[/tex]

Divide both sides by four. Hence, our inequality is:

[tex]b\geq 9[/tex]

In words, this means that the base must be at least 9 feet long.

Which of these figures has rational symmetry?

Answers

Answer:

a is the answer parallelogram is a rotational symmetry

A would be the answer rational symmetry means it can be rotated by an angle of 0 and 360 degrees and be the same :)

Jamie bought a new pair of jeans for $\$10$ because the price marked was $75\%$ off the original price. What was the original price of the pair of jeans?

Answers

Answer:

$40

Step-by-step explanation:

Let

Original price = x

Selling price = $10

Discount = 75%

Selling price = original price - (Discount * original price)

10 = x - 75% of x

10 = x - 0.75 * x

10 = x - 0.75x

10 = 0.25x

x = 10/0.25

x = 40

Original price = x = $40

(5,8) and (x, 12) slope is -2, find x
PLEASE HELP ASAP

Answers

Answer:

x = 3

Step-by-step explanation:

Understandings:

• Slope Formula

—————————

Use the Slope-Formula to identify the slope

Slope-Formula: y2-y1/x2-x1

Slope-Form: 12 - 8/x - 5

Where Slope = -2

12 - 8/x - 5 = -2

4/x - 5 = - 2

x is a positive number

4/(3)- 5 = - 2
4/-2 = -2

- 4/2 = -2

Which statement about the function
true?
The graph of the function f(x) = 4(x + 3)(x - 1) is shown
below.
O The function is positive for all real values of x where
x < -1.
y
6
NA
The function is negative for all real values of x where
x <-3 and where x > 1.
O The function is positive for all real values of x where
x > 0.
O The function is negative for all real values of x where
X<-3 or x>-1.
2
-6
4
2.
4
6
х
-2
-2
4
6

Answers

I think the answer is B

The function is negative for all real values of x where x < -3 or x > -1 and the domain of the function is -∝ < x < ∝

What are domain and range?

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = - ( x + 3 ) ( x - 1 )   be equation (1)

Now , the values of x which makes the function negative are

when x < -3

f ( x ) = - ( -ve ) ( -ve ) = -ve

when x > 1

f ( x ) = - ( +ve ) ( +ve ) = -ve

So , the domain of the function is all real numbers and -∝ < x < ∝

Hence , the function is solved

To learn more about domain and range click :

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{(2,-3),(3,-1),(2,3),(4,6),(6,6)}


Are the ordered pairs a function or not?

Answers

Answer:

Its a domain

Step-by-step explanation:

Domain:{2,3,4,6}

The lengths of the sides of a triangle are 3, 4, 5. Can the triangle be a right triangle?

Answers

Answer:

Yes it can

Step-by-step explanation:

To check wether it's a right angle triangle we need to apply the Pythagoras theorem

h^2= a^2 +b^2

Hypotenuse is always the longest side so

5^2 = 3^2 + 4^2

This is correct, so the triangle is a right angle triangle

Answer from Gauthmath

Solve the system by substitution
y= 5x− 22
y= 4x− 17

Answers

Answer:

x=5, y=3

Step-by-step explanation:

help which one is the correct one

Answers

Answer:

B.) x^12

Step-by-step explanation:

You don't multiply the exponents when multiplying x^7 × x^5, you add them.

If we add the exponents, we get x^12.

Hope this helps!

If there is something wrong, just let me know.

Suppose you have D12000 to save . You have to save some amount at 10% and the rest at 15% how much should be saved at each rate to yield 12% on the total amount saved

Answers

Answer:

$7200 at 10%

$4800 at 15%

Step-by-step explanation:

Imagine that you are given two linear equations in slope-intercept form. You
notice that the slopes are different, but the yintercepts are the same. How
many solutions would you expect for this system of equations?
O A. 1
O B. cannot be determined
O C. O
D. infinitely many

Answers

Answer:

Option A

Step-by-step explanation:

If the system of equations are,

y = m₁x + b

y = m₂x + b

Since, m₁ ≠ m₂ both the lines will be different (not parallel)

Therefore, the will be at least one solution of the given system of equations.

Option A will be the answer.

what number goes in the blank?? NEED HELP ASAPPP

Answers

The answer is 5 :>>>

The linear equation passing through the point (2,-5) has a slope of 2 is

Answers

Answer:

y = 2x - 9

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 2 , then

y = 2x + c ← is the partial equation

To find c substitute (2, - 5) into the partial equation

- 5 = 4 + c ⇒ c = - 5 - 4 = - 9

y = 2x - 9 ← equation of line

What the length of segment LM

Answers

Answer: LM = 23

Step-by-step explanation:

Solve the algebraic equations:

Line KN: (solve for x)

[tex]14x-3=25[/tex]

move the 3 to the other side with addition

[tex]14x=28[/tex]

divide by 14 to get x by itself

[tex]x=2[/tex]

Now that we have x we can find line KL:

[tex]9(2)+5\\18+5\\23[/tex]

So we now know that KL is 23 units. And we know that KL = LM

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