Question

The value of $\tan 9^{\circ }\cdot \tan {27}^{\circ }\cdot \tan {45}^{\circ }\cdot \tan {63}^{\circ }\cdot \tan {81}^{\circ }$ is

Answer 1

$\tan 9^{\circ }\cdot \tan {27}^{\circ }\cdot \tan {45}^{\circ }\cdot \tan {63}^{\circ }\cdot \tan {81}^{\circ }=\tan 9^{\circ }\cdot \tan {27}^{\circ }\cdot \tan {45}^{\circ }\cdot \tan (90-27{)}^{\circ }\cdot \tan (90-9{)}^{\circ }=\tan 9^{\circ }\cdot \tan {27}^{\circ }\cdot \tan {45}^{\circ }\cdot \cot {27}^{\circ }\cdot \cot 9^{\circ }=(\tan 9^{\circ }\cdot \cot 9^{\circ })\cdot (\tan {27}^{\circ }\cdot \cot {27}^{\circ })\cdot \tan {45}^{\circ }=1\cdot 1\cdot 1=1$