Question

Choose the correct answer from the alternatives given.
The value of $\cot$ ${15}^{\circ }\cot {16}^{\circ }\cot {17}^{\circ }....\cot {74}^{\circ }\cot {75}^{\circ }$ is

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

Answer 1

The correct option is B $1$

Given

$\cot {15}^{\circ }\cot {16}^{\circ }{\cot }^{\circ }\cdots \cot {74}^{\circ }\cot {75}^{\circ }$

$\cot {15}^{\circ }\cot {16}^{\circ }{\cot }^{\circ }\cdots \tan {16}^{\circ }\tan {15}^{\circ }$

$\left(\cot {15}^{\circ }\tan {15}^{\circ }\right)\left(\cot {16}^{\circ }\tan {16}^{\circ }\right)\cdots \cot {45}^{\circ }$

$\left(1\right)\left(1\right)\left(1\right)\cdots \left(1\right)$

$⟹1$