Solve the following equations: -1 - - Vidyadip

Question

Solve the following equations:
$\sin\text{x}\ \tan\text{x}-1\tan\text{x}-\sin\text{x}$

✓

Answer

$\sin\text{x}\ \tan\text{x}-1=\tan\text{x}-\sin\text{x}$
$=\sin\text{x}\ \text{tan}\text{x}-\tan\text{x}+\sin\text{x}-1=0$
$\Rightarrow\tan\text{x}(\sin\text{x}-1)+1(\sin\text{x})-1=0$
$\Rightarrow(\tan\text{x}+1)(\sin\text{x}-1)=0$
$\Rightarrow(\tan\text{x}+1)=0$ or $(\sin\text{x}-1)=0$
$\Rightarrow\tan\text{x}=-1$ or $\sin\text{x}=1$
$\Rightarrow\tan\text{x}=\tan\frac{3\pi}{4}$ or $\sin\text{x}=\sin\frac{\pi}{2}$
$\Rightarrow\text{x}=\text{n}\pi+\frac{3\pi}{4}$ or $\text{x}=\text{n}\pi+(-1)^\text{n}\frac{\pi}{2},\ \text{n}\in\text{Z}$

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