Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Equations1 Mark
Question
Write the general solutions of $\tan^22\text{x}=1.$
✓
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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