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
18sqrt(x)
I'm assuming that 3(sqrt(x))5 is equal to 15sqrt(x). If that is the case, just perform the multiplication within each term and treat the sqrt(x) as a variable when you add the all together. It is okay because they are like terms.
The answer would be C.
If you do -5.5 + 2.5 over 6.1 - 3.1 it would be -3 over 3 which is equal to -1.
You could also do -2.5 + 5.5 over 3.1 - 6.1. It would be 3 over -3 which is also equal to -1.
