Question

If $\tan \left(\frac{\pi }{2}\sin \theta \right)=\cot \left(\frac{\pi }{2}\cos \theta \right)$, then $\sin \theta +\cos \theta =$

• A. $2n-1$
• B. $2n+1$
• C. $2n$
• D. $n$

Answer 1

Answer: (B)

$\tan \left(\frac{\pi }{2}\sin \theta \right)=\cot \left(\frac{\pi }{2}\cos \theta \right)$
$\therefore \tan \left(\frac{\pi }{2}\sin \theta \right)=\tan \left(\frac{\pi }{2}-\frac{\pi }{2}\cos \theta \right)$
$\therefore \frac{\pi }{2}\sin \theta =n\pi +\frac{\pi }{2}-\frac{\pi }{2}\cos \theta$
$\sin \theta +\cos \theta =2n+1$