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Solve the Following Equation: 2 Cos 2 X − 5 Cos X + 2 = 0 - Mathematics

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Question

Solve the following equation:

\[2 \cos^2 x - 5 \cos x + 2 = 0\]
Sum
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Solution

\[2 \cos^2 x - 5 \cos x + 2 = 0\]

\[ \Rightarrow 2 \cos^2 x - 4 \cos x - \cos x + 2 = 0\]

\[ \Rightarrow 2 \cos x ( \cos x - 2) - 1 ( \cos x - 2) = 0\]

\[ \Rightarrow (\cos x - 2) ( 2 \cos\theta - 1) = 0\]

\[\Rightarrow ( \cos x - 2 ) = 0\] or
\[( 2 \cos x - 1) = 0\]
\[\cos x = 2\]  is not possible.

\[\therefore 2 \cos x - 1 = 0 \]

\[ \Rightarrow \cos x = \frac{1}{2} \]

\[ \Rightarrow \cos x = \cos \frac{\pi}{3} \]

\[ \Rightarrow x = 2n\pi \pm \frac{\pi}{3}, n \in Z\]

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Chapter 11: Trigonometric equations - Exercise 11.1 [Page 22]

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RD Sharma Mathematics [English] Class 11
Chapter 11 Trigonometric equations
Exercise 11.1 | Q 3.2 | Page 22

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