Question

Value of $\cot 5^{\circ }\cot 10^{\circ }\dots ..\cot 85^{\circ }$ is

• A. 0
• B. -1
• C. 1
• D. 2

Answer 1

Answer: (C)

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