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Question

The value of sin1+sin3+sin5+sin7cos1cos2 sin4 is

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Solution

Given:
sin1+sin3+sin5+sin7cos1cos2sin4

=(sin1+sin5)+(sin3+sin7)cos1cos2sin4
=2sin3cos2+2sin5cos2cos1cos2sin4
=2cos2(sin3+sin5)cos1cos2sin4
=4cos2cos1sin4cos1cos2sin4
=4

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