Question

Please prove that cos2x/-----

Answer 1

Hello!

Here u go...

✔LHS=cos(2x) / 1 + sin(2x) 

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

{
since we have,

cos(2x) = cos^2x-sin^2x

and

cos^2x+sin^2 = 1
}

✔LHS =(cosx+sinx).(cosx -sinx) /(cosx +sinx)^2 

=(cosx -sinx) /(cosx +sinx) 

=(1 -sinx/cosx) /(1 +sinx/cosx) 

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

✔Now

RHS=tan (pi/4 - x) 

=(tanpi/4 - tanx)/(1+tanpi/4tanx) 

=(1-tanx)/(1+tanx)----------(2)

✔from equation (1) and (2) we get,
LHS = RHS.

✔Hope this answer will help u...

@Neha...