Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Equations1 Mark
Question
Write the general solutions of $\tan^22\text{x}=1.$
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Answer
$\Rightarrow\tan^22\text{x}=1$ $\Rightarrow\tan^22\text{x}-1=0$ $\Rightarrow(\tan2\text{x}-1)(\tan2\text{x}+1)=0$ $\Rightarrow\tan2\text{x}=1$ or $\tan2\text{x}=-1$ $\Rightarrow\tan2\text{x}=\tan\frac{\pi}{4}$ or $\tan2\text{x}=-\tan\Big(\frac{\pi}{4}\Big)=\tan\Big(\pi-\frac{\pi}{4}\Big)$ $=\tan\Big(\frac{3\pi}{4}\Big)$ $\therefore2\text{x}=\text{x}\pi+\frac{\pi}{4}$ or $2\text{x}=\text{x}\pi+\frac{3\pi}{4},\text{x}\in\mathcal{Z}$ $\Rightarrow\text{x}=\frac{\text{x}\pi}{2}+\frac{\pi}{8}$ or $\text{x}=\frac{\text{x}\pi}{2}+\frac{3\pi}{8}$ $\Rightarrow\text{x}=\frac{\text{x}\pi}{2}+\frac{\pi}{8},\text{x}\in\text{z}$
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