Question

The value of $(1-\cos \theta )(1+\cos \theta )\left(1+{\cot }^2\theta \right)$ when $\theta =$ $\frac{\pi }{15}$ is

• A. 1
• B. $\frac{1}{2}$
• C. $\frac{-1}{\sqrt{3}}$
• D. 2

Answer 1

Answer: (A)

$(1-\cos \theta )(1+\cos \theta )\left(1+{\cot }^2\theta \right)$
$=\left(1-{\cos }^2\theta \right)\left({\text{cosec}}^2\theta \right)$
$={\sin }^2\theta \cdot {\text{cosec}}^2\theta$
$=1,\forall \theta$