The value of ( 9^ + 81^ ) ( 9^ + cosec\,81^ ) 56^ 34^ + 25^ cosec\,65^ is:

Answer: Option C

$$\begin{array}{rl}& \frac{\left(\cos 9^{\circ }+\sin {81}^{\circ }\right)\left(\sec 9^{\circ }+\text{cosec}{81}^{\circ }\right)}{\sin {56}^{\circ }\sec {34}^{\circ }+\cos {25}^{\circ }\text{cosec}{65}^{\circ }}\\ & =\frac{\left(\cos 9^{\circ }+\cos 9^{\circ }\right)\left(\sec 9^{\circ }+\sec 9^{\circ }\right)}{\cos {34}^{\circ }\sec {34}^{\circ }+\cos {25}^{\circ }\sec {25}^{\circ }}\\ & =\frac{2\cos 9^{\circ }\times 2\sec 9^{\circ }}{1+1}\\ & =\frac{4\times \cos 9^{\circ }\sec 9^{\circ }}{2}\\ & =2\end{array}$$