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Find the General Solution of the Following Equation: C O S E C X = − √ 2

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Question

Find the general solution of the following equation:

\[cosec x = - \sqrt{2}\]
Sum
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Solution

We have:

\[cosecx = - \sqrt{2}\] (or) 
\[\sin x = - \frac{1}{\sqrt{2}}\]
The value of x satisfying 
\[\sin x = - \frac{1}{\sqrt{2}}\] is \[- \frac{\pi}{4}\]
∴ \[\sin x = - \frac{1}{\sqrt{2}}\]
⇒ \[\sin x = \sin ( - \frac{\pi}{4})\]
⇒ \[x = n\pi + \left( - 1 \right)^n \left( - \frac{\pi}{4} \right)\]
 
\[n \in Z\]
⇒ \[x = n\pi + ( - 1 )^{n + 1} \frac{\pi}{4}, n \in Z\]
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Chapter 11: Trigonometric equations - Exercise 11.1 [Page 21]

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R.D. Sharma Mathematics [English] Class 11
Chapter 11 Trigonometric equations
Exercise 11.1 | Q 1.3 | Page 21

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