Question

Show that $cos\theta [\frac{1}{-1sin\Theta }-\frac{1}{1+sin\Theta }]$ can be written in the form k and tan$\Theta$ and find the work of value

Answer 1

We have,

$\cos \theta [\frac{1}{1-\sin \theta }-\frac{1}{1+\sin \theta }]=k\tan \theta$

$\cos \theta \left[\frac{1+\sin \theta -1+\sin \theta }{1-{\sin }^2\theta }\right]=k\tan \theta$

$\cos \theta \frac{2\sin \theta }{{\cos }^2\theta }=k\tan \theta$

$2\tan \theta =k\tan \theta$

$k=2$

Hence, this is the answer.