LHS (1 + sin x)/cos x
= (1+ sin x) /√(1-sin² x) / cos² x + sin² x = 1
= (1 + sin x)² /[√(1-sin x)(1+sin x)]² / squared both sides
= (1+ sin x)/(1-sin x)
RHS cos x/1-sin x
= √(1-sin² x)/(1-sin x)
= √(1-sin x)(1+ sin x)/( 1-sin x)
= [√(1-sinx)(1+sin x)]²/(1-sinx)² / squared both sides
= (1+sin)/(1-sin x)
so LHS = RHS
