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The principal value of ‘ $θ$ ’ for which $2 T a n^{- 1} (\cos θ) = T a n^{- 1} (2 \cos c e θ)$

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π4

π6

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Correct option is A

We have 2Tan-1cosθ=Tan-12cosecθ ⇒Tan-12cosθ1-cos2θ=Tan-12sinθ⇒Tan-12cosθ1-cos2θ=Tan-12sinθ⇒2cosθsin2θ=2sinθ⇒cotθ=1⇒θ=π4

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The principal value of ‘θ’ for which 2Tan−1cosθ=Tan−12cosce θ

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The principal value of ‘ $θ$ ’ for which $2 T a n^{- 1} (\cos θ) = T a n^{- 1} (2 \cos c e θ)$