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

Question

Solve the following equations:
$\tan3\text{x}+\tan\text{x}=2\tan2\text{x}$

✓

Answer

$\tan3\text{x}+\tan\text{x}=2\tan2\text{x}$
$\Rightarrow\tan3\text{x}-\tan2\text{x}=\tan2\text{x}-\tan\text{x}$
$\Rightarrow\tan3\text{x}-\tan2\text{x}=\tan2\text{x}-\tan\text{x}$
$\Rightarrow2\sin^{2}\text{x}\sin2\text{x}=0$
$\Rightarrow\text{Either}$
$\sin\text{x}=0$ or $\sin2\text{x}=0$
$\Rightarrow\text{x}=\text{n}\pi,\text{n}\in\text{z}$ or $2\text{x}=\text{m}\pi,\text{m}\in\text{z}$
$\Rightarrow\text{x}=\text{n}\pi,\text{n}\in\text{z}$ or $\text{x}=\text{m}\frac{\pi}{2},\text{m}\in\text{z}$

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