Question

( begin{array}{l}begin{aligned} &=operatorname{cosec} x(sec x-1)-cot x(1-cos x) &=operatorname{cosec}left(frac{1}{cos x}-1right)-cot x(1-cos x) &=frac{operatorname{cosec} x(1-cos x)-cos (1-cos x)}{cos x} &=(1-cos x)left(frac{operatorname{cosec} x}{cos x}-cot xright) &=(1-cos x)left(frac{1}{sin x cos x}-frac{cos x}{sin x}right) &=(1-cos x) frac{left(cos 1-cos ^{2} xright)}{sin x cos x} &=frac{(1-cos x) sin ^{2} x}{sin x cos x}=frac{operatorname{sen} x-sin x cos x}{cos x} end{aligned} = & tan x-sin xend{array} )
Hence, proved.

# Proven cosec (secx 1) cotult wsi) tann sinn

Solution