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Find the General Solution of the Following Equation: √ 3 Sec X = 2 - Mathematics

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Question

Find the general solution of the following equation:

\[\sqrt{3} \sec x = 2\]
Sum
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Solution

We have:

\[\sqrt{3} \sec x = 2\]
⇒ \[\sec x = \frac{2}{\sqrt{3}}\] (or) 
\[\cos x = \frac{\sqrt{3}}{2}\]
The value of x satisfying \[\cos x = \frac{\sqrt{3}}{2}\] is \[\frac{\pi}{6}\].
∴ \[\cos x = \frac{\sqrt{3}}{2}\]
⇒ \[\cos x = \cos\frac{\pi}{6}\]
⇒ \[x = 2n\pi \pm \frac{\pi}{6}\],
\[n \in Z\]
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Chapter 11: Trigonometric equations - Exercise 11.1 [Page 21]

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RD Sharma Mathematics [English] Class 11
Chapter 11 Trigonometric equations
Exercise 11.1 | Q 1.6 | Page 21

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