The value of (cosec a - sin a)(sec a - cos a)(tan a + cot a) is?

Answer: Option D

(cosec a - sin a) (sec a - cos a) (tan a + cot a)
Put a = 45°
⇒ (cosec45° - sin45°) (sec45° - cos45°) (tan45° + cot45°)
$$\begin{array}{rl}& \Rightarrow \left(\sqrt{2}-\frac{1}{\sqrt{2}}\right)\left(\sqrt{2}-\frac{1}{\sqrt{2}}\right)\left(1+1\right)\\ & \Rightarrow \frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}}\times 2\\ & \Rightarrow \frac{1}{2}\times 2\\ & \Rightarrow 1\end{array}$$