Question

Determine whether sec x -tanxsinx=cosx is a possible identity

Answer 1

`\text{L.H.S}\\\\\sec x - \tan x \sin x\\\\\\=(1)/(\cos x)- (\sin x )/( \cos x ) \cdot \sin x\\\\\\=\frac 1{\cos x} - (\sin^2 x)/(\cos x)\\\\\\=(1- \sin^2 x)/(\cos x)\\\\\\=(\cos^2 x)/(\cos x)~~~~~~~~~~~~~;[\sin^2 x + \cos^2 x = 1]\\\\\\=\cos x\\\\\\=\text{R.H.S}\\\\\text{Since both sides are equal, the given equation is an identity.}`