The solution set of cotθ=−3,cosecθ=2 is

cotθ=− 3,cosecθ=2θ in Q2, principal value of θ =π−π6=5π6∴θ=2nπ+5π6,n∈Z

The solution set of cotθ=−3,cosecθ=2 is

cotθ=− 3,cosecθ=2θ in Q2, principal value of θ =π−π6=5π6∴θ=2nπ+5π6,n∈Z

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The solution set of $\cot θ = - \sqrt{3}, cosec θ = 2$ is

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$\{2 n π + \frac{5 π}{6} : n \in Z\}$

$\{2 n π + \frac{3 π}{4} : n \in Z\}$

$\{2 n π + \frac{2 π}{3} : n \in Z\}$

$\{2 n π + \frac{7 π}{6} : n \in Z\}$

answer is D.

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Detailed Solution

$\cot θ = - \sqrt{3}, cosec θ = 2$

$θ {in Q}_{2}$ , principal value of $θ = π - \frac{π}{6}$

$= \frac{5 π}{6}$

$∴ θ = 2 n π + \frac{5 π}{6}, n \in Z$

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The solution set of cotθ=−3,cosecθ=2 is

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The solution set of $\cot θ = - \sqrt{3}, cosec θ = 2$ is