Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Equations3 Marks
Question
Find the general solutions of the following equations: $\sin\text{x}=\tan\text{x}$
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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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