What are the steps to answering this problem? Sinx(Cosx)/(1+cosx) (1-cosx)= cotx
Verify the following identity:
sin(x) (cos(x))/((1+cos(x)) (1-cos(x))) = cot(x)
Write cotangent as cosine/sine:
(cos(x) sin(x))/((1-cos(x)) (1+cos(x))) = ^?(cos(x))/(sin(x))
Cross multiply:
cos(x) sin(x)^2 = ^?cos(x) (1-cos(x)) (1+cos(x))
Divide both sides by cos(x):
sin(x)^2 = ^?(1-cos(x)) (1+cos(x))
sin(x)^2 = 1-cos(x)^2:
1-cos(x)^2 = ^?(1-cos(x)) (1+cos(x))
(1-cos(x)) (1+cos(x)) = 1-cos(x)^2:
1-cos(x)^2 = ^?1-cos(x)^2
The left hand side and right hand side are identical:
Answer: |(identity has been verified)
