Find the general solutions of the following equations:cosec x=-2 - Vidyadip

Question

Find the general solutions of the following equations:$\text{cosec }\text{x}=-\sqrt{2}$

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Answer

$\text{cosec }\text{x}=-\sqrt{2}$$\Rightarrow\frac{1}{\sin\theta}=-\sqrt{2}$
$\Rightarrow\sin\theta=-\frac{1}{\sqrt2}$
$\Rightarrow\sin\theta=\sin\Big(\pi+\frac{\pi}{4}\Big)$
$\Rightarrow\sin\theta=\sin\frac{5\pi}{4}\text{or}\sin\theta=\sin\Big(-\frac{\pi}{4}\Big)$$\because\sin(-\theta)=-\sin\theta$
$\therefore\theta=\text{n}\pi+(-1)^{\text{n+1}}\frac{\pi}{4},\text{n}\in\text{z}$

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