The value of sin264° + cos64°sin26° + 2cos43°cosec47° is:

Answer: Option D

$$\begin{array}{rl}& {\sin }^{2}64^{\circ }+\cos 64^{\circ }\sin 26^{\circ }+2\cos 43^{\circ }\text{cosec}47^{\circ }\\ & \Rightarrow {\sin }^{2}64^{\circ }+\cos 64^{\circ }\sin \left({90}^{\circ }-{64}^{\circ }\right)+2\cos 43^{\circ }\text{cosec}\left({90}^{\circ }-{43}^{\circ }\right)\\ & \Rightarrow {\sin }^{2}64^{\circ }+\cos 64^{\circ }\cos 64^{\circ }+2\cos 43^{\circ }\sec 43^{\circ }\\ & \Rightarrow {\sin }^{2}64^{\circ }+{\cos }^{2}64^{\circ }+2\cos 43^{\circ }\left(\frac{1}{\cos {43}^{\circ }}\right)\\ & \Rightarrow 1+2\\ & \Rightarrow 3\end{array}$$