Question

$(1-\cos \theta )(1+\cos \theta )(1+{\cot }^2\theta )=?$

• A. $\cos \theta$
• B. $1$
• C. $2$
• D. $\cot \theta$

Answer 1

The correct option is B $1$

$\Rightarrow (1-\cos \theta )(1+\cos \theta )(1+{\cot }^2\theta )$

$\Rightarrow (1-{\cos }^2\theta )(1+{\cot }^2\theta )$

$\Rightarrow ({\sin }^2\theta +{\cos }^2\theta -{\cos }^2\theta )\left({\text{cosec}}^2\theta \right)$

$\Rightarrow \left({\sin }^2\theta \right)\left({\text{cosec}}^2\theta \right)$

$\Rightarrow \left({\sin }^2\theta \right)\left(\frac{1}{{\sin }^2\theta }\right)$

$\Rightarrow 1$