If$\ \frac{3\pi}{4}

Question

If$\ \frac{3\pi}{4} < \alpha < \pi,\ then\ \sqrt{cosec^{2}\alpha + 2\cot\alpha}\$is equal to

Dr. Abubacker · Accepted Answer

(c)
We have, $\sqrt{cosec^{2}\alpha + 2\cot\alpha}$
$= \sqrt{1 + \cot^{2}{\alpha + 2\cot\alpha}} = \left| 1 + \cot\alpha \right|$
But $\frac{3\pi}{4} < \alpha < \pi$
$\Rightarrow \cot{\alpha < - 1\  \Rightarrow 1 + \cot{\alpha < 0}}$
Hence, $\left| 1 + \cot\alpha \right| = \  - (1 + \cot{\alpha)}$

Q. If$\ \frac{3\pi}{4} < \alpha < \pi,\ then\ \sqrt{cosec^{2}\alpha + 2\cot\alpha}\$is equal to

Explanation

Reviewed by Dr. Abubacker

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