Question

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

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

Answer 1

The correct option is D -1

$(\cos \theta -1)(1+\cos \theta )(1+{\cot }^2\theta )$
= $({\cos }^2\theta -1)(1+{\cot }^2\theta )$
= $-{\sin }^2\theta cose{c}^2\theta$ (since, $si{n}^2\theta +co{s}^2\theta =1$ and $cose{c}^2\theta -co{t}^2\theta =1$)
= $-1$