The value of the following is : $${\left( {\frac{{{\text{sin 4}}{{\text{7}}^ \circ }}}{{\cos {{43}^ \circ }}}} \right)^2}$$   + $${\left( {\frac{{\cos {{43}^ \circ }}}{{{\text{sin }}{{47}^ \circ }}}} \right)^2}$$   - $$4{\text{co}}{{\text{s}}^2}{45^ \circ }$$   = ?

Solution (By Examveda Team)

$$\eqalign{ & {\left( {\frac{{{\text{sin 4}}{{\text{7}}^ \circ }}}{{\cos {{43}^ \circ }}}} \right)^2} + {\left( {\frac{{\cos {{43}^ \circ }}}{{{\text{sin }}{{47}^ \circ }}}} \right)^2} - 4{\text{co}}{{\text{s}}^2}{45^ \circ } \cr & = {\left( {\frac{{{\text{cos 4}}{{\text{3}}^ \circ }}}{{\cos {{43}^ \circ }}}} \right)^2} + {\left( {\frac{{sin{{47}^ \circ }}}{{{\text{sin }}{{47}^ \circ }}}} \right)^2} - 4 \times \frac{1}{2} \cr & = 1 + 1 - 2 \cr & = 0 \cr & {\bf{Note:}} \cr & \left( {\sin \left( {{{90}^ \circ } - \theta } \right)} \right) = \cos \theta \cr} $$