Question #18291

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Answer 1 · 2017-01-18T01:54:40

$LHS=(1-cos2x +sin2x)/(1+cos2x +sin2x)$

using formula $1-cos2x=2sin^2x and 1+cos2x=2cos^2x$

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

$=(2sinx(sinx +cosx))/(2cosx(cosx +sinx)$

$=(cancel2sinxcancel((sinx +cosx)))/(cancel2cosxcancel((cosx +sinx))$

$=sinx/cosx$

$=tanx=RHS$

Proved