The value of tan10°. tan15°. tan75°. tan80° is?

Solution (By Examveda Team)

$$\eqalign{ & \tan {10^ \circ }.\tan {15^ \circ }.\tan {75^ \circ }.\tan {80^ \circ } \cr & \Rightarrow \left( {\tan {{10}^ \circ }.\tan {{80}^ \circ }} \right).\left( {\tan {{15}^ \circ }.\tan {{75}^ \circ }} \right) \cr & \Rightarrow 1 \times 1 \cr & \left[ {{\text{If tan A}}{\text{.tan B}} = {\text{1}}{\text{. then, A}} + {\text{B}} = {{90}^ \circ }} \right] \cr & \Rightarrow 1 \cr} $$