The value of cot 18° ( cot 7 2^ .co s^222^ + 1 tan 7 2^ . se c^268^ ) is?

Answer: Option A

$$\cot 18^{\circ }\left(\cot {72}^{\circ }.{\cos }^2{22}^{\circ }+\frac{1}{\tan {72}^{\circ }.{\sec }^2{68}^{\circ }}\right)$$
$$\Rightarrow \cot 18^{\circ }\left(\cot {72}^{\circ }.{\cos }^2{22}^{\circ }+\cot {72}^{\circ }.{\cos }^2{68}^{\circ }\right)$$
$$\Rightarrow \cot 18^{\circ }.\cot 72^{\circ }\left({\cos }^2{22}^{\circ }+{\cos }^2{68}^{\circ }\right)$$
We know that, cotA.cotB = 1 and cos²A + cos²B = 1( when A + B = 90° )
= 1 × 1 = 1