Answer:
sqrt(2)/2
Step-by-step explanation:
Given tan(x)=2-cot(x), find sin(x).
Rewrite in terms of sine and cosine:
sin(x)/cos(x)=2-cos(x)/sin(x)
Multiply both sides by cos(x)sin(x):
sin^2(x)=2sin(x)cos(x)-cos^2(x)
Rewrite cos^2(x) using the identity sin^2(x)+cos^2(x)=1:
sin^2(x)=2sin(x)cos(x)-(1-sin^2(x))
Distribute:
sin^2(x)=2sin(x)cos(x)-1+sin^2(x)
Subtracting sin^2(x) on both sides:
0=2sin(x)cos(x)-1
Add 1 on both sides:
1=2sin(x)cos(x)
Use identity sin(2x)=2sin(x)cos(x) to rewrite right:
1=sin(2x)
Since sin(pi/2)=1, then 2x=pi/2.
Dividing both sides by 2 gives x=pi/4.
So sin(pi/4)=sqrt(2)/2
Answer:
2 1/2x + 1
Step-by-step explanation:
9x -7/2x-3x +1 = 9x - 3 1/2x - 3x + 1 = 2 1/2x + 1
Answer:
1 is the answer
Step-by-step explanation:
-5-(-6) = x
-5 + 6 = x
1 = x
Answer:
Maggie is 13 years old.
Step-by-step explanation:
Maggie's age is: x
Maggie's brother's age is: 2x - 3
The sum of the ages = 36
x + 2x - 3 = 36
3x - 3 = 36
3x = 39
x = 13
Answer: Maggie is 13 years old.
