Question

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

• A. 0
• B. 1
• C. 2
• D.

Answer 1

The correct option is B

1

$\tan \theta \cot \theta =1,$

$\tan (90-\theta )=cot\theta$

and $tan{45}^{\circ }=1$

Given: $tan{1}^{\circ }$.$tan{2}^{\circ }$,$tan{3}^{\circ }$ .......$tan{88}^{\circ }$. $tan{89}^{\circ }$

= ($tan{1}^{\circ }$. $tan{89}^{\circ }$),($tan{2}^{\circ }$. $tan{88}^{\circ }$).....($tan{44}^{\circ }$.$tan{46}^{\circ }$) ($tan{45}^{\circ }$)

= [($tan{1}^{\circ }$. $tan({90}^{\circ }-1^{\circ }$)] . [($tan{2}^{\circ }$. $tan({90}^{\circ }-2^{\circ }$)]..........[($tan{44}^{\circ }$. $tan({90}^{\circ }-{44}^{\circ }$)].1

= ($tan{1}^{\circ }$. $cot{1}^{\circ }$). ($tan{2}^{\circ }$. $cot{2}^{\circ }$) ....... ($tan{44}^{\circ }$. $cot{44}^{\circ }$)

= 1