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

1 Answer
Nghi N. ยท Nghi N
Nov 4, 2015

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

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