The value of $$\frac{{\sin {{25}^ \circ }.\cos {{65}^ \circ } + \cos {{25}^ \circ }.\sin {{65}^ \circ }}}{{{{\tan }^2}{{70}^ \circ } - {\text{cose}}{{\text{c}}^2}{{20}^ \circ }}}$$       is?

Solution(By Examveda Team)

$$\frac{{\sin {{25}^ \circ }.\cos {{65}^ \circ } + \cos {{25}^ \circ }.\sin {{65}^ \circ }}}{{{{\tan }^2}{{70}^ \circ } - \cos e{c^2}{{20}^ \circ }}}$$
$$ = \frac{{\sin {{25}^ \circ }.\cos \left( {{{90}^ \circ } - {{25}^ \circ }} \right) + \,\cos {{25}^ \circ }.\,\sin \left( {{{90}^ \circ } - {{25}^ \circ }} \right)}}{{{{\tan }^2}{{70}^ \circ } - {\text{cose}}{{\text{c}}^2}\left( {{{90}^ \circ } - {{70}^ \circ }} \right)}}$$
$$\eqalign{ & = \frac{{{{\sin }^2}{{25}^ \circ } + {{\cos }^2}{{25}^ \circ }}}{{{{\tan }^2}{{70}^ \circ } - se{c^2}{{70}^ \circ }}} \cr & = \frac{1}{{ - 1}} \cr & = - 1 \cr} $$