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Question

sinA+sin2A+sin4A+sin5AcosA+cos2A+cos4A+cos5A=tanxA. Find x

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Solution

sinA+sin2A+sin4A+sin5AcosA+cos2A+cos4A+cos5A

=(sin5A+sinA)+(sin4A+sin2A)(cos5A+cosA)+(cos4A+cos2A)

we know that sinC+sinD=2sinC+D2cosCD2
sinCsinD=2cosC+D2sinCD2

=2sin3Acos2A+2sin3AcosA2cos3Acos2A+2cos3AcosA
=2sin3A(cos2A+cosA)2cos3A(cos2A+cosA)=tan3A=tanxA

x=3
Ans: 3

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