Question

The value of tan $1^{\circ }$ tan $2^{\circ }$ tan $3^{\circ }$$\times ..........\times$tan ${89}^{\circ }$ is

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

Answer 1

The correct option is B $1$

$\tan 1^{\circ }\tan 2^{\circ }\tan 3^{\circ }\times ..........\times \tan {89}^{\circ }$
$=\left(\tan 1^{\circ }\tan {89}^{\circ }\right)\left(\tan 2^{\circ }\tan {88}^{\circ }\right)\times ....\times \tan {45}^{\circ }$
$=\left(\tan 1^{\circ }\cot 1^{\circ }\right)\left(\tan 2^{\circ }\cot 2^{\circ }\right)\times ...\times \tan {45}^{\circ }$ $[\because \tan \theta =\cot ({90}^{\circ }-\theta )$ and $\tan \theta \times \cot \theta =1]$
$=1$