Question

General solution of the equation $2{\cot }^{2}x={\text{cosec}}^{2}x$ is :

• A. $n\pi \pm \frac{\pi }{6},n\in Z$
• B. $n\pi \pm \frac{\pi }{2},n\in Z$
• C. $n\pi \pm \frac{\pi }{4},n\in Z$
• D. $n\pi \pm \frac{3\pi }{4},n\in Z$

Answer 1

The correct option is C $n\pi \pm \frac{\pi }{4},n\in Z$

$2{\cot }^{2}x={\text{cosec}}^{2}x\Rightarrow {\cot }^{2}x={\text{cosec}}^{2}x-{\cot }^{2}x\Rightarrow {\cot }^{2}x=1\Rightarrow {\tan }^{2}x=1\Rightarrow x=n\pi \pm \frac{\pi }{4},n\in Z$