Question

Verify The Identity?

Verify this identity:
sin^2(x/2)=(csc^2(x)-cot^2(x))/(2csc^2(x)+2csc(x)cot(x))

Answer 1

See proof below

Explanation:

The right hand side is

`{csc^2(x) -cot^2(x)}/{2csc^2(x)+2csc(x)cot(x)} = {(csc(x)-cot(x))(csc(x)+cot(x))}/{2 csx(x) ( csx(x)+cot(x))} = 1/2{csc(x) -cot(x)}/csc(x) = 1/2(1-cos(x)) = 1/2(1-{1-2sin^2(x/2)})=sin^2(x/2)`