Question #452ac

1 Answer
Jan 25, 2018

Explained below.

Explanation:

It would be easier to prove RHS equal to LHS. Accordingly,

RHS=1/(cos 2x) - (2tan x)/ (1-tan^2x)1cos2x2tanx1tan2x

=1/(cos^2 x - sin^2 x) - (2sin x cosx)/(cos^2x - sin^2x)1cos2xsin2x2sinxcosxcos2xsin2x

= (1- 2sinx cos x)/(cos^2 x - sin^2 x)12sinxcosxcos2xsin2x

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

=(cosx- sinx)/(cos x+ sin x)cosxsinxcosx+sinx =LHS