Question

The value of $\tan 1^0\tan 2^0\tan 3^0.....\tan {89}^0$

• A. $1$
• B. $0$
• C. $\infty$
• D. $\frac{1}{2}$

Answer 1

Answer: (A)

$1$

We know $\tan {89}^0=\cot 1^0;\tan {88}^0=\cot 2^0$ etc
Therefore, $\tan 1^0\tan 2^0\tan 3^0....\tan {88}^0\tan {89}^0$
$=\left(\tan 1^0\cot 1^0\right)\left(\tan 2^0\cot 2^0\right)...\tan {45}^0$
$=1$ ....[Since $\tan 45=1$]