Question

If $2\sec 2\theta =\tan \varphi +\cot \varphi ,$ then a value of $\theta +\varphi$ is

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{3}$
• D. $\pi$

Answer 1

Answer: (B)

Given $2\sec 2\theta =\tan \varphi +\cot \varphi$
$\Rightarrow 2\sec 2\theta =2cosec2\varphi$
$\Rightarrow \sec 2\theta =cosec2\varphi$
$\Rightarrow \sec 2\theta =\sec \left(\frac{\pi }{2}-2\varphi \right)$
$\Rightarrow 2\theta =\frac{\pi }{2}-2\varphi$