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Question

Prove that sinx+sin3xcosx+cos3x=tan2x

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Solution

sinx+sin3xcosx+cos3x=tan2x
L.H.S=sinx+sin3xcosx+cos3x
cosA+cosB=2cos(A+B2)cos(AB2)
sinA+sinB=2sin(A+B2)cos(AB2)
=2sin(x+3x2)cos(x3x2)2cos(x+3x2)cos(x3x2)
=sin(x+3x2)cos(x+3x2)
=tan2x=R.H.S
Hence proved.

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