What is the value of 50^ 40^ + 3 cosec\, 80^ 10^ - 2 50^ cosec\,40^ ?

Answer: Option A

$$\begin{array}{rl}& \frac{\cos {50}^{\circ }}{\sin {40}^{\circ }}+\frac{3\text{cosec}\text{8}{0}^{\circ }}{\sec {10}^{\circ }}-2\cos 50^{\circ }\cdot \text{cosec}40^{\circ }\text{ angle of sum}=90^{\circ }\\ & \text{then,}\\ & =\frac{\sin {40}^{\circ }}{\sin {40}^{\circ }}+\frac{3\text{cosec}\text{5}{0}^{\circ }}{\text{cosec}\text{8}{0}^{\circ }}-2\sin 40^{\circ }\cdot \text{cosec}10^{\circ }\\ & =1+3-2\\ & =2\end{array}$$