How do you prove (1+tanx) /( 1-tanx) = (1+sin2x) / cos"2x"?

1 Answer
May 27, 2016

as follows

Explanation:

RHS= (1+sin2x) / cos"2x"

Inserting ,1=(cos^2x+sin^2x) and cos2x=(cos^2x-sin^2x)

RHS = (cos^2x+sin^2x+2sinxcosx) / (cos^2x-sin^2x)

= (cosx+sinx)^2 /( (cosx-sinx)xx (cosx+sinx))

= (cosx+sinx)^cancel2 /( (cosx-sinx)xx cancel(cosx+sinx))

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

Dividing both numerator and denominator by cosx

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

= (1+tanx) / (1-tanx)=LHS
proved