Question

If $2{\cot }^2\theta ={\csc }^2\theta$, then the general value of $\theta$ is-

• A. $n\pi \pm \frac{\pi }{4}$
• B. $2n\pi \pm \frac{\pi }{4}$
• C. $n\pi +(-1{)}^n\frac{\pi }{4}$
• D. $2n\pi \pm \frac{\pi }{2}$

Answer 1

Answer: (B)

$2n\pi \pm \frac{\pi }{4}$

Simplifying $2{\cot }^2\theta ={\csc }^2\theta$

$2\frac{{\cos }^2\theta }{{\sin }^2\theta }=\frac{1}{{\sin }^2\theta }$

$2{\cos }^2\theta =1$

${\cos }^2\theta =\frac{1}{2}$

$\cos \theta =\frac{1}{\sqrt{2}}$

$\cos \theta =\cos \frac{\pi }{4}$

$\theta =2n\pi \pm \frac{\pi }{4}$