Question

$\frac{\tan \theta }{1-\cot \theta }+\frac{\cot \theta }{1-\tan \theta }-\sec \theta cosec\theta =$.

Answer 1

$\frac{{\tan }^2\theta }{\tan \theta -1}-\frac{\cot \theta }{\tan \theta -1}-\sec \theta cosec\theta$

$\frac{{\sin }^2\theta }{\cos \theta (\sin \theta -\cos \theta )}-\frac{{\cos }^2\theta }{\sin \theta (\cos \theta -\sin \theta )}-\frac{1}{\sin \theta \cos \theta }$

$\frac{{\sin }^3\theta -{\cos }^3\theta }{\sin \theta \cos \theta (\sin \theta -\cos \theta )}-\frac{1}{\sin \theta \cos \theta }$

$\frac{1-2\sin \theta \cos \theta +3\sin \theta \cos \theta }{\sin \theta \cos \theta }-\frac{1}{\sin \theta \cos \theta }$

$⟹1$