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Question

cosA+cos3A+cos5A+cos7AsinA+sin3A+sin5A+sin7A=

A
sin 4A
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B
cos 4A
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C
tan 4A
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D
cot 4A
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Solution

The correct option is D cot 4A
G.E=(cosA+cos5A)+(cos3A+cos7A)(sinA+sin5A)+(sin3A+sin7A=2cos3A cos2A+2cos5A cos2A2sin3A cos2A+2sin5A cos2A

=2cos2A(cos3A+cos 5A)2cos2a(sin3A+sin5A)=2cos 4AcosA2sin 4A cosA=cot 4A

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