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Solve the Following Equation: Cos X + Cos 3 X − Cos 2 X = 0

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प्रश्न

Solve the following equation:

\[\cos x + \cos 3x - \cos 2x = 0\]
योग
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उत्तर

\[\cos x + \cos 3x - \cos 2x = 0\]
\[\Rightarrow 2 \cos \left( \frac{4x}{2} \right) \cos \left( \frac{2x}{2} \right) - \cos2x = 0\]
\[ \Rightarrow 2 \cos2x \cos x - \cos2x = 0\]
\[ \Rightarrow \cos2x ( 2 \cos x - 1) = 0\]

\[\Rightarrow \cos2x = 0\] or

\[2 \cos x - 1 = 0\]
\[\Rightarrow \cos2x = \cos \frac{\pi}{2}\] or
\[\cos x = \frac{1}{2} \Rightarrow \cos x = \cos\frac{\pi}{3}\]
\[\Rightarrow 2x = (2n + 1)\frac{\pi}{2}, n \in Z\] or
\[x = 2m\pi \pm \frac{\pi}{3}, m \in Z\]
\[\Rightarrow x = (2n + 1)\frac{\pi}{4}, n \in Z\] or
\[x = 2m\pi \pm \frac{\pi}{3}, m \in Z\]
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अध्याय 11: Trigonometric equations - Exercise 11.1 [पृष्ठ २२]

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आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 11 Trigonometric equations
Exercise 11.1 | Q 4.2 | पृष्ठ २२

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