The value of $$\left( {{{\sin }^2}7{{\frac{1}{2}}^ \circ } + {{\sin }^2}82{{\frac{1}{2}}^ \circ }} \right)$$     is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{If A + B}} = {90^ \circ } \cr & {\text{Then,}}{\sin ^2}{\text{A + }}{\sin ^2}{\text{B}} = 1 \cr & \Rightarrow 7{\frac{1}{2}^ \circ } + 82{\frac{1}{2}^ \circ } \cr & \Rightarrow {90^ \circ } \cr & \Rightarrow 1\left[ {{\text{sin }}{{90}^ \circ } = 1} \right] \cr} $$