If sin(θ + 18°) = cos60° (0° < θ < 90°), then the value of cos 5θ is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{sin}}\left( {\theta + {{18}^ \circ }} \right) = \cos {60^ \circ }\left( {{0^ \circ } < \theta < {{90}^ \circ }} \right) \cr & \Rightarrow \theta + {18^ \circ } + {60^ \circ } = {90^ \circ } \cr & \Rightarrow \theta = {12^ \circ } \cr & \Rightarrow {\text{cos 5}}\theta {\text{ }} \cr & \Rightarrow {\text{cos }}{60^ \circ } \cr & \Rightarrow \frac{1}{2} \cr} $$