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

Solution (By Examveda Team)

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