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Find the General Solution of the Following Equation: Sec X = √ 2

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Question

Find the general solution of the following equation:

\[\sec x = \sqrt{2}\]
Sum
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Solution

We have:
\[\sec x = \sqrt{2}\] (or) 

\[\cos x = \frac{1}{\sqrt{2}}\]
The value of x satisfying \[\cos x = \frac{1}{\sqrt{2}}\] is \[\frac{\pi}{4}\]
∴ \[\cos x = \frac{1}{\sqrt{2}}\]
⇒ \[\cos x = \cos \frac{\pi}{4}\]
⇒ \[x = 2n\pi \pm \frac{\pi}{4}\],
\[n \in Z\]
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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 1.4 | Page 21

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