If $$\frac{sec^{2}\ 70^\circ-cot^{2}\ 20^\circ}{2\ (cosec^{2}\ 59^\circ-tan^{2}\ 31^\circ)}=\frac{2}{m}$$, then m is equal to

Expression : $$\frac{sec^{2}\ 70^\circ-cot^{2}\ 20^\circ}{2\ (cosec^{2}\ 59^\circ-tan^{2}\ 31^\circ)}=\frac{m}{2}$$

Using, $$cot(90^\circ-\ \theta)=tan\ \theta$$ and vice-versa

= $$\frac{sec^{2}\ 70^\circ-cot^{2}\ (90^\circ-70^\circ)}{2[\ cosec^{2}\ 59^\circ-tan^{2}(90^\circ- 59^\circ)]}=\frac{m}{2}$$

= $$\frac{sec^{2}\ 70^\circ-tan^{2}\ 70^\circ}{2\ (cosec^{2}\ 59^\circ-cot^{2}\ 59^\circ)}=\frac{m}{2}$$

Using, $$(sec^2\ \theta-tan^2\ \theta=1)$$ and $$(cosec^2\ \theta-cot^2\ \theta=1)$$

= $$\frac{1}{2\times1}=\frac{m}{2}$$

=> $$m=1$$

=> Ans - (C)