Question

The numerical value of $(1-\cos x)(1+\cos x)(1+{\cot }^{2}x)$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is B $1$

Given, $(1-\cos x)(1+\cos x)(1+{\cot }^{2}x)$

$\text{using}(A+B)(A-B)=A^2-B^2$
and $({\text{cosec}}^{2}x-{\cot }^{2}x)=1$

$\Rightarrow (1-{\cos }^{2}x)\left({\text{cosec}}^{2}x\right)$

Now, using $({\sin }^{2}x+{\cos }^{2}x)=1$

$\Rightarrow {\sin }^{2}x.{\text{cosec}}^{2}x=1$