Find the general solutions of the following equations: = - Vidyadip

Question

Find the general solutions of the following equations:
$\sin\text{x}=\tan\text{x}$

✓

Answer

We have,

$\sin\text{x}=\tan\text{x}$

$\Rightarrow\sin\text{x}=\frac{\sin\text{x}}{\cos\text{x}}$

$\Rightarrow\sin\text{x}=\frac{\sin\text{x}}{\cos\text{x}}=0$

$\Rightarrow\sin\text{x}(\cos\text{x}-1)=0$

$\Rightarrow$ Either $\sin\text{x}=0$ or $\cos\text{x}-1=0$

Now,

$\Rightarrow\text{x}=\text{n}\pi,\text{n}\in\text{z}$ or $\cos\text{x}=1$

$\Rightarrow\cos\text{x}=\cos0^\circ$

$\text{x}=2\text{m}\pi,\text{m}\in\text{z}$

Thus,

$\text{x}=\text{n}\pi\text{n}\in\text{z}$ or $\text{x}=2\text{m}\pi,\text{m}\in\text{z}$

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