Sec x - cos x = sin x tan x

Question

Verify the identity by proving the left-hand side is the same as the right-hand side

Answer 1

general approach is convert everything into sines and cosines

secx = 1/cosx, so left side is 1/cosx - cosx = (1-cos^2x)/cosx=(cos^2x+ sin^2x -cos^2x)/cosx = sin^2x/cosx

cos^2x + sin^2x = 1, above replaced 1 by it's equivalent in sines and cosines

on the right side, tanx= sinx/cosx so tanxsinx = (sinx/cosx)sinx = sin^2x/cosx which is the same as the left side