If 3 4, then cosec 2 + 2 cot is equal to

Question

If $\frac{3 π}{4} < α < π,$ then $\sqrt{\cos e c^{2} α + 2 c o t α}$ is equal to

Smart Achievers · Accepted Answer

(3)

We have, $\sqrt{c o s e c^{2} α + 2 \cot α}$

$= \sqrt{1 + \cot^{2} α + 2 \cot α}$

$=$ $| 1 + \cot α |$

But $\frac{3 π}{4} < α < π$

$\Rightarrow$ $\cot α < - 1$

$\Rightarrow$ $1 + \cot α < 0$

Hence, $| 1 + \cot α |$ $= - (1 + \cot α)$

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