Verify the identity sin 2xcos 2x 1 tan x SolutionLHS sin2x

Verify the identity: sin 2x/cos 2x + 1 = tan x

Solution

LHS

sin2x/(cos2x+1)

=(2sinxcosx)/(cos²x-sin²x +1)

=(2sinxcosx)/(cos²x+1-sin²x )

=(2sinxcosx)/(cos²x+cos²x )................(since sin²x +cos²x =1)

=(2sinxcosx)/(2cos²x)

=(2sinxcosx)/(2cosxcosx)

cancel out 2cosx in numerator and denominator

=(sinx)/(cosx)

=tanx

RHS