Solve the following equations: + 3x- 2x=0 - Vidyadip

Question

Solve the following equations: $\cos\text{x}+\cos3\text{x}-\cos2\text{x}=0$

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Answer

$\cos\text{x}+\cos3\text{x}-\cos2\text{x}=0$
$\Rightarrow2\cos2\text{x}.\cos\text{x}-\cos2\text{x}=0$
$\Rightarrow\cos2\theta(2\cos\theta-1)=1$
Either
$\cos2\theta=0\ \text{or}\ 2\cos\theta=1$
$\Rightarrow2\theta=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{ z}$or $\cos\theta=\frac{1}{2}=\cos\frac{\pi}{3}$
$\Rightarrow\theta=(2\text{n}+1)\frac{\pi}{4},\text{n }\in\ \text{z}$ or $\theta=2\text{m}\pi\pm\frac{\pi}{3},\text{m }\in\ \text{z}$

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