Question

Value of the expression
$(1-\cos \theta )(1+\cos \theta )(1+{\cot }^2\theta )$ is

• A. $0$
• B. $1$
• C. ${\sin }^2\theta$
• D. ${\csc }^2\theta$

Answer 1

The correct option is B $1$

$(1-\cos \theta )(1+\cos \theta )(1+{\cot }^2\theta )$
$=(1-{\cos }^2\theta )\left({\csc }^2\theta \right)$
$=\left({\sin }^2\theta \right)\left({\csc }^2\theta \right)$
$=1$
Hence answer is B