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Question

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

A
tan2A
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B
cot3A
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C
tan3A
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D
tan4A
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Solution

The correct option is C tan3A
sinA+sin2A+sin4A+sin5AcosA+cos2A+cos4A+cos5A
=(sinA+sin5A)+(sin4A+sin2A)(cos5A+cosA)+(cos4A+cos2A)
=2sin3Acos2A+2sin3AcosA2cos3Acos2A+2cos3AcosA
=2sin3A(cos2A+cosA)2cos3A(cos2A+cosA)
=tan3A

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