show-that-1-cosecx-cotx-1-cosecx-cotx-2cosecx-

Question Number 31016 by 78987 last updated on 02/Mar/18

s h o w t h a t 1 / cosec x - c o t x + 1 / cosec x + \cot x = 2 cosec x

Answered by iv@0uja last updated on 02/Mar/18

\frac{1}{cosec x - \cot x} + \frac{1}{cosec x + \cot x}

= \frac{1}{\frac{1}{\sin x} - \frac{\cos x}{\sin x}} + \frac{1}{\frac{1}{\sin x} + \frac{\cos x}{\sin x}}

= \frac{\sin x}{1 - \cos x} + \frac{\sin x}{1 + \cos x}

= \frac{(1 + \cos x) \sin x + (1 - \cos x) \sin x}{1 - \cos^{2} x}

= \frac{2 \sin x}{\sin^{2} x} = \frac{2}{\sin x} = 2 cosec x

Facebook Tweet Pin