How do you prove tan2x + sec2x = (cosx + sinx) / (cosx – sinx)?

1 Answer
Jul 1, 2016

As below

Explanation:

RHS = (cosx + sinx) / (cosx – sinx)

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

= (cosx + sinx) ^2/ (cos^2x – sin^2x)

= (cos^2x + sin^2x+2sinxcosx) / (cos2x)

=(1+sin2x)/(cos2x)=1/(cos2x)+(sin2x)/(cos2x)

=tan2x+sec2x=LHS

proved