Question

The value of $\tan 1^{\circ }\tan 2^{\circ }.....\tan {89}^{\circ }$ is .....

• A. $1$
• B. $-1$
• C. $0$
• D. $2$

Answer 1

The correct option is A $1$

Rearranging the expression
$=\left(\tan 1^{\circ }\tan {89}^{\circ }\right)\left(\tan 2^{\circ }\tan {88}^{\circ }\right)......\left(\tan {44}^{\circ }\tan {46}^{\circ }\right)\tan {45}^{\circ }$
$=\left(\tan 1^{\circ }\tan \right({90}^{\circ }-1\left)\right(\tan 2^{\circ }\tan ({90}^{\circ }-2^{\circ })).....(\tan {44}^{\circ }\tan ({90}^{\circ }-{44}^{\circ })\tan {45}^{\circ }$
$=\tan 1^{\circ }\cot 1^{\circ }\tan 2^{\circ }\cot 2^{\circ }.....\tan {44}^{\circ }\cot {44}^{\circ }\times \tan {45}^{\circ }$
$=1\times \mathrm{1.....}1\times 1$
$=1$
So $1$ is correct.