How do you prove that $\frac{1 - cos x}{sin x} = \frac{sin x}{1 + cos x}$ $(1-cosx)/sinx = sinx/(1+cosx)$ ?

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How do you prove that $\frac{1 - cos x}{sin x} = \frac{sin x}{1 + cos x}$ $(1-cosx)/sinx = sinx/(1+cosx)$ ?

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Answer 1 · 2015-04-14T01:22:54

Start from the Trig Identity "1 - cos^2 x = sin^2 x".
(1 - cos^2 x) = sin^2 x
(1 - cos x)(1 + cos x) = sin xsin x
Divide both sides by (sin x)(1 + cos x)
(1 - cos x)/sinx = sin x/(1 + cos x)

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How do you prove that $\frac{1 - cos x}{sin x} = \frac{sin x}{1 + cos x}$ $(1-cosx)/sinx = sinx/(1+cosx)$ ?

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How do you prove that $\frac{1 - cos x}{sin x} = \frac{sin x}{1 + cos x}$ $(1-cosx)/sinx = sinx/(1+cosx)$ ?