Simplification of this trigonometric expression: $\tan(1°)×\tan(2°)×\tan(3°)×\tan(4°)×\cdots×\tan(87°)×\tan(88°)×\tan(89°)$

Question

$$\tan(1°)×\tan(2°)×\tan(3°)×\tan(4°)×\cdots×\tan(87°)×\tan(88°)×\tan(89°)$$

What I tried is that I firstly changed all the $\tan$ to $\dfrac{\sin}{\cos}$ but I got stuck along the way..

Please help me guys

Answer 1

Hint: $$ \tan{(90-x)} = \frac{\sin{(90-x)}}{\cos{(90-x)}} = \frac{\cos{x}}{\sin{x}} = \frac{1}{\tan{x}}. $$