Question #7218e

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Answer 1 · 2016-04-16T21:29:43

See below

LHS=left hand side, RHS =right hand side

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

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

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

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

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

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

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

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

$=sinx$

$=RHS$