Prove each of the following identities (a) sec x + tan x =cos x/1 − sin x (b) tan^2 x/tan^2 x + 1= sin^2 x?

1 Answer
Jul 16, 2018

a)

LHS=sec x + tan x

=1/cosx + sinx/cosx

=((1 + sinx)cosx)/cos^2x

=((1 + sinx)cosx)/(1-sin^2x)

=((1 + sinx)cosx)/((1-sinx)(1+sinx))

=cos x/(1 − sin x)=RHS

(b) LHS=tan^2 x/(tan^2 x + 1)

=tan^2 x/sec^2 x

=(sin^2 x/cos^2x)/(1/cos^2 x

= sin^2 x=RHS