Proof-that-1-cos-x-1-cos-x-1-cos-x-1-cos-x-2-cosec-x-

Question Number 176164 by HeferH last updated on 14/Sep/22

P r o o f t h a t :

\sqrt{\frac{1 - \cos x}{1 + \cos x}} + \sqrt{\frac{1 + \cos x}{1 - \cos x}} = 2 \cdot cosec x

Answered by Rasheed.Sindhi last updated on 14/Sep/22

\sqrt{\frac{1 - \cos x}{1 + \cos x}} + \sqrt{\frac{1 + \cos x}{1 - \cos x}} = 2 \cdot cosec x

LHS : \frac{\sqrt{1 - \cos x}}{\sqrt{1 + \cos x}} + \frac{\sqrt{1 + \cos x}}{\sqrt{1 - \cos x}}

= \frac{1 - \cos x + 1 + \cos x}{\sqrt{1 - \cos^{2} x}}

= \frac{2}{\sin x}

= 2 \cdot \frac{1}{\sin x}

= 2 cosec x = RHS