If ^270^ - co t^220^ 2 ( cose c^259^ - ^231^ ) = 2/m , then m is equal to?

Answer: Option C

$$\begin{array}{rl}& \frac{{\sec }^2{70}^{\circ }-\text{co}{\text{t}}^2{20}^{\circ }}{2\left(\text{cose}{\text{c}}^2{59}^{\circ }-{\tan }^2{31}^{\circ }\right)}=\frac{2}{m}\\ & \Rightarrow \frac{{\sec }^2{70}^{\circ }-\text{co}{\text{t}}^2\left({90}^{\circ }-{70}^{\circ }\right)}{2\left(\text{cose}{\text{c}}^2{59}^{\circ }-{\tan }^2\left({90}^{\circ }-{59}^{\circ }\right)\right)}=\frac{2}{m}\\ & \Rightarrow \frac{{\sec }^2{70}^{\circ }-\text{ta}{\text{n}}^2{70}^{\circ }}{2\left(\text{cose}{\text{c}}^2{59}^{\circ }-{\cot }^2{59}^{\circ }\right)}=\frac{2}{m}\\ & \Rightarrow \frac{1}{2}=\frac{2}{m}\left[{\sec }^2\theta -\text{ta}{\text{n}}^2\theta =1\right]\\ & (cose{c}^2\theta -{\cot }^2\theta =1)\\ & \Rightarrow m=2\times 2\\ & \Rightarrow m=4\end{array}$$