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Question

Prove the following:
cos(3π2+x)cos(2π+x)[cot(3π2x)+cot(2π+x)]=1

Solution
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LHS=cos(3π2+x)cos(2π+x)[cot(3π2x)+cot(2π+x)]

=sinxcosx[tanx+cotx]

=sinxcosx(sin2x+cos2x)sinxcosx=1=RHS

Hence proved

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