Question

The value of $cot{5}^{\circ }cot{10}^{\circ }...........cot{85}^{\circ }$ is

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

Answer 1

Answer: (B)

1

Given that $\cot 5^{\circ }\cot {10}^{\circ }...........\cot {85}^{\circ }$
$=\cot 5^{\circ }\cot {10}^{\circ }.........\cot ({90}^{\circ }-{10}^{\circ })\cot ({90}^{\circ }-5^{\circ })$
$=\cot 5^{\circ }\cot {10}^{\circ }.........\tan {10}^{\circ }\tan 5^{\circ }$
$=\left(\tan 5^{\circ }\cot 5^{\circ }\right)\left(\tan {10}^{\circ }\cot {10}^{\circ }\right)............\left(\cot {45}^{\circ }\right)$
$=\left(1\right)\left(1\right)\left(1\right).......\left(1\right)=1$