Question

The value of $tan1^{\circ}\, tan2^{\circ}\, tan3^{\circ} \ldots \, tan89^{\circ}$ is

• A. $0$
• B. $1$
• C. $\frac{1}{2}$
• D. Not defined

Answer 1

Answer: (B)

$1$

Answer 2

$tan\,1^{\circ} \cdot tan2^{\circ} \cdot tan3^{\circ} \ldots \, tan89^{\circ}$ $=\left(tan\,1^{\circ}\,tan\,89^{\circ}\right)\left(tan\,2^{\circ}\,tan\,88^{\circ}\right)\ldots\left(tan\,44^{\circ}\,tan\,46^{\circ}\right)tan\,45^{\circ}$ $=\left(tan\,1^{\circ}\,cot1^{\circ}\right)\left(tan2^{\circ}\,cot2^{\circ}\right)\ldots tan\,45^{\circ}=1\cdot1 \ldots 1=1$