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Question

If sinA+sin2A=x,cosA=x,cosA+cos2A=y,
then prove that - (x2+y2)(x2+y23)=2y.

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Solution

Substituting values
[(sinA+sin2A)2+(cosA+cos2A)2][(sinA+sin2A)2+(cosA+cos2A)23]
=[1+1+cosAcos3A+cos3A+cosA][2+2cosA3]
=(2+2cosA)(2cosA1)
=4cosA2+4cosA2cosA
=4cos2A+2cosA2
=2(2cos2A1)+2cosA
=2cos2A+2cosA
=2(cosA+cos2A)=2y
Hence proved.

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