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  4. If tan ((π/2) sin θ)= cot ((π/2) cos θ), then sin θ+ cos θ=

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

Trigonometric Functions

Solution:

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