Question

Show that sinxtanx=1-cos^2x/cosx

Answer 1

LHS: = $\sin x \tan x = \frac{\sin x \sin x }{\cos x} = \frac{\sin^2 x}{\cos x}$ (using $\tan x = \frac{\sin x}{\cos x}$)

We know $\sin^2x + \cos^2x = 1 \Rightarrow \sin^2x=1-\cos^2x$ so we can replace the sin²x in the LHS expression as follows

$\frac{\sin^2x}{\cos x} = \frac{1-\cos^2x}{\cos x}$ which is the RHS.