The value of sin²64° + cos64°sin26° + 2cos43°cosec47° is:

Solution (By Examveda Team)

$$\eqalign{ & {\sin ^2}{64^ \circ } + \cos {64^ \circ }\sin {26^ \circ } + 2\cos {43^ \circ }{\text{cosec}}\,{47^ \circ } \cr & \Rightarrow {\sin ^2}{64^ \circ } + \cos {64^ \circ }\sin \left( {{{90}^ \circ } - {{64}^ \circ }} \right) + 2\cos {43^ \circ }{\text{cosec}}\left( {{{90}^ \circ } - {{43}^ \circ }} \right) \cr & \Rightarrow {\sin ^2}{64^ \circ } + \cos {64^ \circ }\cos {64^ \circ } + 2\cos {43^ \circ }\sec {43^ \circ } \cr & \Rightarrow {\sin ^2}{64^ \circ } + {\cos ^2}{64^ \circ } + 2\cos {43^ \circ }\left( {\frac{1}{{\cos {{43}^ \circ }}}} \right) \cr & \Rightarrow 1 + 2 \cr & \Rightarrow 3 \cr} $$