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Question

If tan(π cos x) = cot (π sin x), prove that cos(xπ4)=±122

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Solution

tan(πcosx)=cot(πsinx)tan(πcosx)=tan(π2πsinx)cosx=12sinxcosx+sinx=1212cosx+12sinx=±122cosπ4cosx+sinπ4sinx=±122cos(xπ4)=±122

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