What is the value of ( 180 - ) ( 90 - ) + ( 90 - )1 + ^2 ?

Answer: Option A

$$\begin{array}{rl}& \sin \left(180-\theta \right)\sin \left(90-\theta \right)+\frac{\cot \left(90-\theta \right)}{1+{\tan }^2\theta }\\ & \Rightarrow \sin \theta \cos \theta +\frac{\tan \theta }{{\sec }^2\theta }\\ & \Rightarrow \sin \theta \cos \theta +\frac{\sin \theta }{\cos \theta }\times {\cos }^2\theta \\ & \Rightarrow \sin \theta \cos \theta +\sin \theta \cos \theta \\ & \Rightarrow 2\cos \theta \sin \theta \end{array}$$