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Answer 1 · 2016-04-16T21:29:43

See below

LHS=left hand side, RHS =right hand side

LHS=#(sin(2x+x))/(1+2cos2x)#

#=(sin2xcosx+cos2xsinx)/(1+2cos2x)#

#=((2sinxcosx)cosx+(1-2sin^2x)sinx)/(1+2cos2x)#

#=(2sinxcos^2x+sinx-2sin^3x)/(1+2(1-2sin^2x))#

#=(2sinx(1-sin^2x)+sinx-2sin^3x)/(1+2-4sin^2x)#

#=(2sinx-2sin^3x+sinx-2sin^3x)/(3-4sin^2x)#

#=(3sinx-4sin^3x)/(3-4sin^2x)#

#=(sinx(3-4sin^2x))/(3-4sin^2x)#

#=sinx#

#=RHS#