Solve the following equations: + =2 - Vidyadip

Question

Solve the following equations:
$\cot\text{x}+\tan\text{x}=2$

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Answer

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

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