Question #9a6e1

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Answer 1 · 2018-02-20T08:19:38

Please see below.

#LHS=(1+sinx-cosx)^2/(1+sinx+cosx)^2#

#=(1+2(sinx-cosx)+(sinx-cosx)^2)/(1+2(sinx+cosx)+(sinx+cosx)^2#

#=(1+2(sinx-cosx)+sin^2x+2sinx*cosx+cos^2x)/(1+2(sinx+cosx)+(sin^2x+2sinx*cosx+cos^2x)#

#=(2+2(sinx-cosx)+2sinx*cosx)/(2+2(sinx+cosx)+2sinx*cosx)#

#=(1+sinx-cosx+sinx*cosx)/(1+sinx+cosx+sinx*cosx)#

#=(1-cosx+sinx(1+sinx))/(1+cosx+sinx(1+sinx)#

#=((1-cosx)(1+sinx))/((1+cosx)(1+sinx))#

#=(1-cosx)/(1+cosx)=RHS#

Answer 2 · 2018-02-20T08:35:09

#LHS=(1+sinx-cosx)^2/(1+sinx+cosx)^2#

#=(2sin^2(x/2)+2sin(x/2)cos(x/2))^2/(2cos^2(x/2)+2sin(x/2)cos(x/2))^2#

#=(4sin^2(x/2)cancel((sin(x/2)+cos(x/2))^2))/(4cos^2(x/2)cancel((sin(x/2)+cos(x/2))^2))#

#=(cancel2(1-cosx))/(cancel2(1+cosx))=RHS#