Question

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

• A. 0
• B. 1
• C. 2
• D. 1/2

Answer 1

Answer: (B)

1

since $\tan {89}^{\circ }=\cot 1^{\circ }\tan {88}^{\circ }=\cot 2^{\circ }$
In the seires
total 89 terms and middle term is $\tan {45}^o$
$\tan 1^o\times \tan {89}^o=\tan 1^o\times \cot 1^o=1$
$\tan 2^o\times \tan {88}^o=\tan 2^o\times \cot 2^o=1$
..............................
..............................
$\tan {44}^o\times \tan {46}^o=\tan {44}^o\times \cot {44}^o=1$
$\therefore \tan 1^{\circ }\tan 2^{\circ }...\tan {89}^{\circ }=1$