Question

How do you verify `(1 - cos x) / (1 + cos x) = (csc x - cot x)^2`?

Answer 1

Verify `(1 - cos x)/(1 + cos x) = (csc x - cot x)^2`

Explanation:

Multiply both numerator and denominator of left side by (1 - cos x).
`((1 - cos x)/(1 + cos x))((1 - cos x)/(1 - cos x)) =`
`= (1 - cos x)^2/(1 - cos^2 x) = (1 - cos x)^2/(sin^2 x) =`
`= ((1- cos x)/(sin x))^2 = (1/(sin x) - (cos x/sin x))^2 =`
`= (csc x - cot x)^2`