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Question

Prove that cos7x+cos5xsin7xsin5x=cotx

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Solution

Applying the trigonometric identities in the LHS of the cos7x+cos5xsin7xsin5x=cotx.

cos7x+cos5xsin7xsin5x=2cos6xcosx2cos6xsinx

=cosxsinx

=cotx

=RHS


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