General solution of 5x= 2x is : - Vidyadip

MCQ

General solution of $\tan5\text{x}=\cot2\text{x}$ is :

A
$\frac{\text{n}\pi}{7}+\frac{\pi}{2},\ \text{n}\in\text{Z}$
B
$\text{x}=\frac{\text{n}\pi}{7}+\frac{\pi}{3},\ \text{n}\in\text{Z}$
✓
$\text{x}=\frac{\text{n}\pi}{7}+\frac{\pi}{14},\ \text{n}\in\text{Z}$
D
$\text{x}=\frac{\text{n}\pi}{7}=\frac{\pi}{14},\ \text{n}\in\text{Z}$

✓

Answer

Correct option: C.

$\text{x}=\frac{\text{n}\pi}{7}+\frac{\pi}{14},\ \text{n}\in\text{Z}$

Given :
$\tan5\text{x}=\cot2\text{x}$
$\Rightarrow\tan5\text{x}=\tan\Big(\frac{\pi}{2}-2\text{x}\Big)$
$\Rightarrow5\text{x}=\text{n}\pi+\frac{\pi}{2}-2\text{x}$
$\Rightarrow7\text{x}=\text{n}\pi+\frac{\pi}{2}$
$\Rightarrow\text{x}=\frac{\text{n}\pi}{7}+\frac{\pi}{14},\ \text{n}\in\text{Z}$

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