prove that (tan²y) (cos²y) + 1/sec²y = 1​

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

tan x = [tex]\frac{sinx}{cosx}[/tex] , sec x = [tex]\frac{1}{cosx}[/tex] , sin²x + cos²x = 1

Consider the left side

tan²y × cos²y + [tex]\frac{1}{sec^2y}[/tex]

= [tex]\frac{sin^2y}{cos^2y}[/tex] × cos²y + [tex]\frac{1}{\frac{1}{cos^2y} }[/tex] ← cancel cos²y in the product

= sin²y + cos²y

= 1

= right side ⇒ proven

Answer 2

Step-by-step explanation:

[tex] (\tan^2y) (\cos^2y) +\frac{1}{\sec^2y} = 1\\

LHS

= (\tan^2y) (\cos^2y) +\frac{1}{\sec^2y} \\\\

\frac{\sin^2y}{\cos^2y}\times \cos^2 y + \cos^2 y \\\\

= \sin^2y + \cos^2 y \\\\

= 1\\\\

= RHS\\\\

\purple {\boxed {\bold {\therefore (\tan^2y) (\cos^2y) +\frac{1}{\sec^2y} = 1}}} \\[/tex]

Hence Proved


Related Questions

When 50 pounds of a compound are produced, the manufacturing cost is described by x
and the selling price is described by x^2 + 8x - 20.
What is ratio of the cost to the selling price when x = 50?

Answers

Answer:

45

Step-by-step explanation:

y

The answer is 45 hope this helps buddy

1. What side in the second trapezoid corresponds to CD?
choices:
RU
ST
TU
RS

2. What angle in the second trapezoid corresponds to B?

choices:
T
S
U
R



Answers

Answer:

1...ut

2..s

Step-by-step explanation:

you can see that the trapezium ABCD is talented than you are St trapezium so then from the ABCD trapezium Appa what then you can see a De is parallel to you are and ab is parallel to AC and DC is parallel parallel to T s and a De is parallel to ur

Answer:

1. UT

2. S

Step-by-step explanation:

1. parallel sides of the first trapezoid are DC and AB, the last being the longest

so the answer is

UT, which is shorter base

2. B is the right angle

so S is the one on the second trapezoid

If you answer can you write how you solved it?

Answers

Answer:

[tex]145.3in^2[/tex]

Step-by-step explanation:

[tex]A_{L} =2\pi rh=2*\pi *2.5*9.25\\=145.3in^2[/tex]

1. Find the volume of both right cylinders.

Answers

1.) 1205.76
2.)653.12

Answer:

the one with 8 and 6= 1206.37

the one with 4 and 13 = 653.45

Step-by-step explanation:

v=[tex]\pi[/tex]r2h

v=[tex]\pi[/tex]8(2)(6)

v=[tex]\pi[/tex]4(2)13

PLS HELP!!!!!! In a survey of 4530 U.S. adults, 87% said that they would like to donate more to charity. What is the margin of error for the survey? Round to the nearest tenth of a percent

Answers

Answer:

Margin of Error = 1.0% to the nearest tenth of a percent.

Step-by-step explanation:

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value is obtained from the z-tables at the popular confidence level of 95% and z-tables is used because the sample size, 4530, is large enough to approximate the population properties.

Critical value = 1.960

Standard error = σₓ = √[p(1-p)/n]

p = 87% = 0.87

n = sample size = 4530

σₓ = √[0.87×0.13)/4530]

= 0.0049966876

Margin of Error = 1.96 × 0.0049966876 = 0.0097935078 = 0.00979 = 0.979% = 1.0% to the nearest tenth of a percent.

Hope this Helps!!!

Which is the angle measure represented by 2 rotations counterclockwise?
a. -1080°
C. 1080°
b. -720°
d. 720°

Answers

-720 because counter clockwise it would be 720 which is 360 times 2 but since it is backwards it’s -720.
I think it is a

Explanation is counterclockwise means going bakwards so that might be right

Aisha is playing a game in which she can gain or lose points on each turn. The table below
shows the points she scores on each of four turns in the game.
Aisha states that her highest score is on Turn 3, because 16 is greater than 3, 10, or 9. Use the
drop-down menus to explain Aisha's mistake.

Answers

Answer:

A score of -16 represents the lowest of points for these four turns.

The number for Aisha's highest score will be turn 2 on the number line.

That number is 10.  

Step-by-step explanation:

Since the options of the drop down menu are not included, you should choose any option similar to lowest.

Aisha's highest score was obtained in turn 2 and that is 10.

Aisha is comparing absolute terms, that is why she believes that -16 represents a good score, while in reality is the worst she got.

6 cm
4 cm
3 cm
12 cm
What’s the purple? Areas

Answers

Answer:

36 cm

Step-by-step explanation:

A = b1 + b2 x h / 1/2

A = 12 + 6 x 4 / 1/2

answer with work pls!!

Answers

The reflected coordinates will be ( 15,7)

Please help ASAP!!!……………………

Answers

-10, -6, -8, -42 are all the correct answers

Answer:

your answer will be -42,-10,-8,-6

What is the surface area of a cone with a radius of 3 meters and a slant of 4

Answers

Answer:

A≈65.97m²

Step-by-step explanation:

A=πrl+πr2=π·3·4+π·32≈65.97345m

!!!!HELP PLS!!!! 19 POINTS
In equation y=15x+12, what is the 15? *
In equation y=15x+12, what is the 12? *
How would you create a table of values for the equation y=15x+12? *

Answers

Answer:

1. Coefficient

2. Constant

3. (0,12)(1,27)(2,42)(3,57)(4,72)

Step-by-step explanation:

If the sum of 4040 consecutive integer numbers is 2020, find out the absolute difference between the first number and the last number.

Answers

Let [tex]x[/tex] be the smallest of the consecutive integers summing to 2020. Then the largest integer in the sum is [tex]x+4039,[/tex] so our answer is [tex]\boxed{4039}.[/tex]

For completeness, though, let's solve for the value of [tex]x[/tex] that satisfies the conditions of the problem. Recall that the sum of an arithmetic series with first term [tex]a_1,[/tex] last term [tex]a_n,[/tex] and [tex]n[/tex] terms, is [tex]\frac{n(a_1+a_n)}{2}.[/tex] Plugging in our known values gives us the equation [tex]\frac{4040(2x+4039)}{2}=2020,[/tex] which simplifies to [tex]2x+4039=1.[/tex] Thus, [tex]x=-2019,[/tex] so the 4040 consecutive integers are [tex]-2019,-2018,\dots,-1,0,1,\dots,2018,2019,2020.[/tex] Notice how everything except the [tex]2020[/tex] cancels out!

Construct one circle with center A passing through point B and another circle with center A passing through C. Circles with common centers are called concentric circles. We’ll refer to the circle that passes through B as AB and the one that passes through C as AC. Besides being concentric, what is the relationship between circles AB and AC? someone please help me

Answers

Answer:

The two circles centered at point A are concentric and similar

Step-by-step explanation:

plato

What is the output or waste of the cellular respiration cycle?

Answers

Answer: The outputs, or products, of cellular respiration are water and carbon dioxide

Explanation: The inputs, or reactants, of cellular respiration are glucose and oxygen. The outputs, or products, of cellular respiration are water, carbon dioxide

The ratio of the measures of two supplementary angles is 8:4. What is the measure of
the smaller angle?

Answers

Answer:

the smaller angle = 4x = 4*15 = 60 degrees

Step-by-step explanation:

In a club there are 10 women and 7 men. A committee of 6 women and 4 men is to be chosen. How many different ways are there to select the committee?

A) 1,680 ways
B) 27 ways
C) 7,350 ways
D) 127,008,000 ways

Answers

Answer:

c

Step-by-step explanation:

10×3×7×7×5=7350ways

A blueberry bush was 13 inches tall. One year later, the bush was 25 inches tall.
Which number sentence shows how many inches the bush grew in one year?

Answers

Answer:

12 inches

Step-by-step explanation:

25-13=12

(How much it grew in the last year.)

Answer:
12 inches

Expression:
25-13

what is

A, 80cm : 2.5

B,4kg : 1600g

C,5m : 500m

d, 800g : 2kg

f, 5days : 5weeks

h,40sec : 1min

j, 800ml : 1l

l, 10cm : 80cm

pls tell me the answers i will give 5stars

Answers

Answer:

......

Step-by-step explanation:

b)4kg:1600g

convert 4kg to grams

4000g:1600g

then divide

=5g:2g

then convert 5g into kg

=0.005kg:2g

f)5 days:5 weeks

multiply 5weeks by 7 u will get 35

5days :35dys then divide by 5

1:7days

=1 day:1 week

h)40 sec:1 min

40 sec:60 sec

then divide both of them by 2

2 sec:3 sec

then take 3 ÷60=0.05 min

=2 sec:0.05 min

A mayor wants to determine if the people in his city think that he is doing a good job. Which choice BEST represents the population? A) Voters age 21 to 35. B) All the local business owners. C) The people who voted for him. D) All the residents of the city. Eliminate

Answers

Answer:

D

Step-by-step explanation:

D is the best choice. A excludes voters age 18-20 and 36+. B excludes everyone who doesn't own a business, and C excludes those who didn't vote for him. For the most honest results, D - everyone - is the best choice.

Solve the problem in the image above

Answers

Answer:

Step-by-step explanation:

3[tex]x^{4}[/tex]

Answer: 9 √(3^x6)

Step-by-step explanation:

HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

[tex]-2\frac{1}{4}=\frac{-9}{4}\\\\-1\frac{1}{2}=\frac{-3}{2}\\\\[/tex]

-2 1/4  ÷ -1 1/2 =

[tex]\frac{-9}{4}*\frac{-2}{3}=\frac{3}{2}*\frac{1}{1}\\\\=\frac{3}{2}\\\\=1\frac{1}{2}[/tex]

Find the area of the equilateral triangle

Answers

Answer:

An equilateral triangle can be defined as a special type of triangle whose all the sides and internal angles are equal. In an equilateral triangle, the measure of internal angles is 60 degrees.

Step-by-step explanation:

Line segments AB and BC are tangents to Circle P. What is the value of x?
a.117
b.73
c.107
d.146

Answers

Answer:

c. 107°

Step-by-step explanation:

In the figure attached, Circle P, segments AB and BC, and angle x are shown.

From circumscribed angle theorem, we know that angle ABC and angle x are supplementary, then:

x + 73° = 180°

x = 180° - 73°

x = 107°

(-4, -5) (3, 4) Slope:



(0, -2) (5, -1) Slope:



(-5, -1) (5, -3) Slope:



(-5, -5) (-1, 5) Slope:



(-2, 0) (4, 1) Slope:
I WILL GIVE BRANLIEST

Answers

Answer    

1.M=1

2.3/5

3.(NO SOLUTION)

4.0

5.1/2 =0.5

Step-by-step explanation:

Y=mx+b

M=(Y2)+(y1)/(x2)+(x1)

1. x1  y1    x2   y2

    (-4 , -5) , (3 , 4)

Slope:

M=(4)+(-5)/(3)+(-4)

=-1/-1= 1

2. x1  y1    x2   y2

    (0 , -2) , (5, -1)

Slope:

M=(-1)+(-2)/(5)+(0)

=-3/5

3. x1  y1    x2   y2

    (-5 , -1) , (5 , -3)

Slope:

M=(-3)+(-1)/(5)+(-5)

=- 4/0=(NO SOLUTION)

4. x1  y1    x2   y2

    (-5, -5) (-1, 5)

Slope:

M=(5)+(-5)/(-1)+(-5)

= 0/-6 =0

5. x1  y1    x2   y2

    (-2, 0) (4, 1)

Slope:

M=(1)+(0)/(4)+(-2)

= 1/2 =0.5

A right angle is equal to how many angles

Answers

Answer:

90 degrees

A right angle is equal to 90 degrees. A line segment (AB) drawn so that it forms right angles with a line (CD).

Step-by-step explanation:

Answer:

3 angles

Step-by-step explanation:

there are 3 angles, one a right angle (90 degrees), and the other two are acute angles (45 degrees)

Tom and Sam can finish a plowing job in two hours. Tom working alone can do the job in 7 hours. How long would it take Sam to finish the same job alone?

Answers

Answer:

Step-by-step explanation:

1X+17=121X+17=12

1X=12−171X=12−17

1X=72×7−27×21X=72×7−27×2

1X=7−2141X=7−214

1X=5141X=514

Taking inverse on both sides

X=145=2.8 hoursX=145=2.8 hours

The time taken by Sam is 2.8 hours.2.8 hours.

Rudolf has a pool that has a diameter of about 24.26 mm. What is the area of the pool in terms of pi

Answers

Answer:

   = 147.1369 pi

Step-by-step explanation:

The diameter is 24.26

The radius is d/2 = 24.26/2 =12.13

The area of a circle is

A = pi r^2

   = pi (12.13)^2

   = 147.1369 pi

Answer:

147.1369

Step-by-step explanation:

i think im wrong not sure. also the answer is not rounded.

which one isn’t a function ?

Answers

Answer:

D isn't a function because points intersect vertically on the graph

Step-by-step explanation:

Estimate a 15% tip on a dinner bill of $81.66 by first rounding the bill amount to the nearest ten dollars.​

Answers

Answer:

12 dollars

Step-by-step explanation:

Round the bill to the nearest ten dollars

81.66 rounds to 80 dollars

80 * 15%

80 *.15

12

The tip is 12 dollars

Answer:

81.66/100*115 = 93.909 rounding down to $90

Step-by-step explanation:

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