Question

Prove that 2 cosec 2x + cosec x = sec x. cot (x/2)​

Answer 1

Step-by-step explanation:

$2cosec2x + cosecx = secx.cot \frac{x}{2} \\ \\ L.H.S\\ 2cosec2x + cosecx \\ \frac{2}{sin2x} + \frac{1}{sinx} \\ \frac{2(1+ cosx)}{2 sinx \: cosx } \\ \frac{2(2 {cos}^{2} \frac{x}{2} )}{4 sin \frac{x}{2} cos \frac{x}{2}cosx } \\ \frac{cos \frac{x}{2} }{ sin \frac{x}{2} cosx } \\ secx.cot \frac{x}{2} \\ \\ Hence \: proved \: \\ Hope \: it \: will \: help \: you$