The value of $\frac{\cos \left(90^{\circ}-\theta\right) \sec \left(90^{\circ}-\theta\right) \tan \theta}{\operatorname{cosec}\left(90^{\circ}-\theta\right) \sin \left(90^{\circ}-\theta\right) \cot \left(90^{\circ}-\theta\right)}+\frac{\tan \left(90^{\circ}-\theta\right)}{\cot \theta}$ is
(a) 1
(b) − 1
(c) 2
(d) −2
We have to find: $\frac{\cos \left(90^{\circ}-\theta\right) \sec \left(90^{\circ}-\theta\right) \tan \theta}{\operatorname{cosec}\left(90^{\circ}-\theta\right) \sin \left(90^{\circ}-\theta\right) \cot \left(90^{\circ}-\theta\right)}+\frac{\tan \left(90^{\circ}-\theta\right)}{\cot \theta}$
So
$\frac{\cos \left(90^{\circ}-\theta\right) \sec \left(90^{\circ}-\theta\right) \tan \theta}{\operatorname{cosec}\left(90^{\circ}-\theta\right) \sin \left(90^{\circ}-\theta\right) \cot \left(90^{\circ}-\theta\right)}+\frac{\tan \left(90^{\circ}-\theta\right)}{\cot \theta}$
$=\frac{\sin \theta \operatorname{cosec} \theta \tan \theta}{\sec \theta \cos \theta \tan \theta}+\frac{\cot \theta}{\cot \theta}$
$=\frac{1 \times \tan \theta}{1 \times \tan \theta}+\frac{\cot \theta}{\cot \theta}$
$=1+1$
$=2$
Hence the correct option is $(c)$
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