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If $\sin (π \cot θ) = \cos (π \tan θ)$ then

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a

cot⁡2θ=14,−34

b

cot⁡2θ=4,43

c

cot⁡2θ=−34,−14

d

none of these

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detailed solution

Correct option is A

We have,sin⁡(πcot⁡θ)=cos⁡(πtan⁡θ)sin⁡(πcot⁡θ)=sin⁡π2+πtan⁡θcos⁡(πtan⁡θ)=cos⁡3π2+πcot⁡θ⇒ πcot⁡θ=π2+πtan⁡θ or, πtan⁡θ=3π2+πcot⁡θ⇒ cot⁡θ−tan⁡θ=12 or, cot⁡θ−tan⁡θ=−32⇒ 1−tan2⁡θ2tan⁡θ=14 or, 1−tan2⁡θ2tan⁡θ=−34⇒ cot⁡2θ=14 or, cot⁡2θ=−34

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