Question

Find the value of tan 1 degree tan 2degree up to tan 89 degree

Answer 1

Answer : 1

Explanation:

$</p><p></p><p>\rightarrow \quad \tan 1^{\circ} \cdot \tan 2^{\circ} \cdot ... \cdot \tan 88^{\circ} \cdot \tan 89^{\circ} \\ \\</p><p></p><p>\rightarrow \quad \cot \left( 90^{\circ} - 1^{\circ} \right) \cdot \cot \left( 90^{\circ} - 2^{\circ} \right) \cdot ... \cdot \frac{1}{\cot 88^{\circ} } \cdot \frac{1}{\cot 89^{\circ}} </p><p></p><p></p><p>\\ \\</p><p></p><p>\rightarrow \quad \cancel{\cot 89^{\circ}} \cdot \cancel{\cot 88^{\circ}} \cdot ... \cdot \frac{1}{\cancel{\cot 88^{\circ} }} \cdot \frac{1}{\cancel{\cot 89^{\circ}}} </p><p>$

And similarly everything cancels out.

Leaving 1 .

So the answer is 1