Answers
Answer:
[tex]\frac{1-\tan x }{1+\cot x}[/tex]
Step-by-step explanation:
Let [tex]\frac{\sin 2x+\cos 2x-1}{\sin 2x+\cos 2x + 1}[/tex], we proceed to prove the given identity by trigonometric and algebraic means:
1) [tex]\frac{\sin 2x+\cos 2x-1}{\sin 2x+\cos 2x + 1}[/tex] Given
2) [tex]\frac{2\cdot \sin x \cdot \cos x +\cos ^{2}x - \sin^{2}x-1}{2\cdot \sin x \cdot \cos x +\cos ^{2}x - \sin^{2}x+1}[/tex] [tex]\sin 2x = 2\cdot \sin x \cdot \cos x[/tex]/[tex]\cos 2x = \cos^{2}x - \sin^{2}x[/tex]
3) [tex]\frac{2\cdot \sin x \cdot \cos x -\sin^{2}x-(1-\cos^{2}x)}{2\cdot \sin x\cdot \cos x +\cos^{2}x+(1-\sin^{2}x)}[/tex] Commutative, associative and distributive properties/[tex]-a = (-1)\cdot a[/tex]
4) [tex]\frac{2\cdot \sin x \cdot \cos x -2\cdot \sin^{2}x}{2\cdot \sin x \cdot \cos x +2\cdot \cos^{2}x}[/tex] [tex]\sin^{2}x + \cos^{2}x = 1[/tex]
5) [tex]\frac{(2\cdot \sin x)\cdot (\cos x-\sin x)}{(2\cdot \cos x)\cdot (\sin x +\cos x)}[/tex] Distributive and associative properties.
6) [tex]\frac{\sin x\cdot (\cos x-\sin x)}{\cos x\cdot (\sin x +\cos x)}[/tex] Existence of multiplicative inverse/Commutative and modulative properties.
7) [tex]\frac{\frac{\cos x -\sin x}{\cos x} }{\frac{\sin x + \cos x}{\sin x} }[/tex] [tex]\frac{\frac{x}{y} }{\frac{w}{z} } = \frac{x\cdot z}{y\cdot w}[/tex]
8) [tex]\frac{\frac{\cos x}{\cos x}-\frac{\sin x}{\cos x} }{\frac{\sin x}{\sin x}+\frac{\cos x}{\sin x} }[/tex] [tex]\frac{x+y}{w} = \frac{x}{w} + \frac{y}{w}[/tex]
9) [tex]\frac{1-\tan x }{1+\cot x}[/tex] Existence of multiplicative inverse/[tex]\tan x = \frac{\sin x}{\cos x}[/tex]/[tex]\cot x = \frac{\cos x}{\sin x}[/tex]/Result
Related Questions
1) Calculate the quotient 2166 / 38
Answers
Answer:
57
Step-by-step explanation:
2166/38=57
Answer: 57
Step-by-step explanation:2188 divided by 38 =57
(2, 1), (4, 3). (6, 5), (8,7)
Answers
Answer:
(1, 2), (3, 4), (5, 6), (8, 7)
Step-by-step explanation:As we can observe from the answers the representation is about the pair of points. We can sort it out by excluding the wrong options.
simplify
5p - 4p - 4p
Answers
Answer:
-3p
Step-by-step explanation:
Answer:
-3p
Step-by-step explanation:
5p - 4p = 1p - 4p = -3p
3 times a number plus 5 is breathers than 12. Graph the possible solutions
Answers
3x12+5 is greater than 12 .
If 3x - 7 = 2, then x equals?
Answers
Answer:
rjogir
grggreijgojrejow
g
Step-by-step explanation:
Answer:
3x - 7 = 2
3x = 2 + 7
3x = 9
x =9/3
x = 3
x equals 3
please help me this is due in 10 minutes i’ll give brainlyist
Answers
Answer:
y=125x+500
Step-by-step explanation: plug the values into x and it's that equation
3,1,-2,-4,-1, least to greatest
Answers
Answer:
-4, -2, -1, 1, 3
Step-by-step explanation:
Because some of these numbers are negative, they will be getting smaller as they get bigger. Think of it like this:
When you are determining whether the negative number is bigger or smaller, take the negative sign off or pretend its not there. Then, as the numbers get bigger, they become less. For example, you have these numbers:
-1, -5, -8, -3, and -2
To find out what the order is from least to greatest, you do this:
take the negative sign off
1,5,8,3, and 2
then put them in order from least to greatest
so its
1, 2, 3, 5, 8
Then flip it so its from greatest to least
so its
8,5,3,2,1
Now put the negative signs back
making it:
-8, -5, -3, -2, and -1
That is how you find out what the numbers are from least to greatest.
Hope this helps!
PS. You should eat chicken nuggets because they are good
HELP FAS, worth 20 points
Answers
Answer:
1. infinite solutions.
2. no solutions.
Step-by-step explanation:
a. 8x + 7 = 8x + 7
The expressions are equal to each other; therefore, the equation has infinite solutions.
b. 10t - 6 = 10t + 6
10t = 10t + 12
0 = 12
These terms do not equal each other. 0 does not equal 12; therefore, this equation has no solutions.
Kathy jumped 16 1/2 ft at the long jump event. Nadia jumped 18 1/8 ft at the long jump. How much farther did Nadia jump than Kathy?
Answers
Answer:
12 ft
Step-by-step explanation:
First you do 16 x 2 +1 and you get 133, second you do 18 x 8 +1 = 145 third you need to subtract 145 - 133, and you get 12 feet.
Hope this helped.
Which expression is equivalent to 0?
(a)(-a)
a +(-a)
a/-a
a - (-a)
Answers
Answer:
a - a or (a +(-a))
Step-by-step explanation:
A negative plus a positive is always zero if they have the same variable.
(a)(-a) equals -a
a/-a equals -a
and
a-(-a) equals positive a
Evaluate when x = -3 and y= -1:
Answers
Answer:
-3 + -1
Step-by-step explanation:
What is the slope of 7; (4 -30)
Answers
Answer:
Can you restate the question, it is hard to solve with typos.
If you would like, it would also help to attach an image or picture of the question.
10, 6, 3, 10, 1
Mode ??
Median ??
Answers
Answer:
Median is 6 Mode is 10
Step-by-step explanation:
Median is the middle number when all the numbers are lined up in order.
Mode is the number that shows up most frequently.
Answer:
Mode: 10
Median: 6
Step-by-step explanation:
Plz help a real one out
Answers
Answer:
Correct answer is A
Step-by-step explanation:
44.72+57.12 = 101.54
180-Ans
= 78.46
Cost of a tie: $35.50
Markup: 30%
Discount: 20%
Tax: 5%
Answers
Answer:
40.25 i believe
Step-by-step explanation:
Three (3) consecutive integers is such that the largest is x. Write an expression
for the smallest.
Answers
Answer:
Consider 3 consecutive integers: (smallest) x, x+1 and x+2 (largest)
Step-by-step explanation:
Five times the smallest means 5x
Sum of the largest and five times the smallest means x+2+5x
This sum is -244 means x+2+5x=-244
Solve this equation
x+2+5x=-244
6x+2=-244
6x=-244-2
6x=-246
x=-41
So, smallest number is -41, second is -40 and largest is -39
You're answer is -39+5(-41)=244
Why I don't have information to find the missing lengths?
Answers
Answer:
yes
Step-by-step explanation:
PLEASE HELP ME IT IS AN EMERGENCY!!!!!!!!! I WILL MARK BRAINLLIEST FOR THE CORRECT ANSWER!!!!!!!!!!!!
When the original price and discounted prices are known, how can we find the percent markdown?
Answers
Step-by-step explanation:
The amount that you decrease the price by can be expressed as a percent of the selling price, known as the markdown rate.
What is the simplified value of the exponential expression 27 1/3
Answers
Answer:
3
Step-by-step explanation:
I need help with this math assignment!! Will mark brainliest!
Answers
Answer:
Sorry but i can't help u.
Step-by-step explanation:
Hari's weekly allowance varies depending on the number of chores he does. He received $20 in allowance the week he did 10 chores, and $16 in allowance the week he did 2 chores. Write an equation for his allowance in slope-intercept form.
Answers
Answer:
y=1/2x+12
Step-by-step explanation:
Answer:
y = 2x + (-30)
Step-by-step explanation:
Find the slope, then find the y-intercept.
But that is for if the points are, (20,10) and (16,2)
If you were finding the equation for the points, (10,20) and (2,16) the equation would be y = 0.5x + 15
1. g(x) = -2(x + 3) 2 - 1
Identify the a,h,k and vertex for each quadratic function
Answers
9514 1404 393
Answer:
a = -2, h = -3, k = -1
vertex = (-3, -1)
Step-by-step explanation:
Compare the given equation ...
g(x) = -2(x +3)² -1
to the vertex form ...
g(x) = a(x -h)² +k
You see that ...
a = -2
-h = +3 ⇒ h = -3
+k = -1 ⇒ k = -1
The vertex is (h, k), so is ...
vertex = (-3, -1)
Taylor has dd dimes and qq quarters. She has a maximum of $4 worth of coins altogether. Write this situation as an inequality.
Answers
Answer: .10d+.25q<_ 4
Step-by-step explanation:
d= dimes and q = quarters
dimes are worth .10 and quarters are worth .25
The inequality for the given situation is
0.1d + 0.251 ≤ 4
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
10 dimes = 1 dollar
1 dime = 0.1 dollar
4 quarters = 1 dollar
1 quarter = 0.25 dollar
Now,
The maximum amount is $4.
So,
0.1d + 0.251 ≤ 4
Thus,
The inequality is 0.1d + 0.251 ≤ 4.
Learn more about inequalities here:
https://brainly.com/question/20383699
#SPJ2
3х + 4y = - 23
х = 3y+1
Solve systems of equations!
Answers
Answer:
[tex]3(3y + 1) + 4y = - 23 \\ 9y + 3 + 4y = - 23 \\ 9y + 4y = - 23 - 3 \\ \frac{13y}{13y} = \frac{ - 26}{13} = - 2[/tex]
In the diagram below AB is parallel to CD what is the value of x
Answers
The value of x is 150°. The correct option is D. 150°
Calculating anglesFrom the question, we are to determine the measure of angle x
In the given diagram, we can observe that
The angle supplementary with x is 30° (Alternate angles theorem)
Thus,
x + 30° = 180° (Supplementary angles)
x = 180° - 30°
x = 150°
Hence, the value of x is 150°. The correct option is D. 150°
Learn more on Calculating angles here: https://brainly.com/question/12060386
#SPJ1
Find the volume of a cylinder that has a diameter of 12 cm and a height of 5
cm. Use 3.14 for pi and round to the nearest tenth. *
Answers
Answer:
V≈565.5cm³ is the answer
Leila and Joe are two partners in a business. Leila makes $3 in profits for every $4 that Jo makes. If Jo makes $32 profit on the first item they sell, how much profit does Leila make?
Answers
Answer:
$24
Step-by-step explanation:
Since 32 divided by 4 equals 8, and 8 times 3 equals 24, if Jo makes $32 profit on the first item they sell, Leila will make $24 profit.
I hope this helps you :D
5. Given the function f(x) = 3(1.55)x.
a. Does the above exponential function represent exponential growth or decay?
b. State the percent increase of the above function.
c. State the growth factor (or multiplier) of the above function.
d. What is the initial amount of f(x)?
Answers
Answer:
it A ;)
Step-by-step explanation:
Factor the expression using the greatest common factor
2x + 10 =
Answers
Answer:
2(x+5)
Step-by-step explanation:
2x+10
1.Factor our the 2 from the equation
2.Your answer after will be 2(x+5)
Answer:
Step-by-step explanation:
Which equation represents 4x – 3y = 15 when solved for y
Answers
Answer:
y=4/3x-5
Step-by-step explanation:
4x-3y=15
-4x -4x
______________
-3y=-4x+15
---- --- ---- (divide all by -3)
-3 -3 -3
y=4/3x-5
