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