The expression (cos⁶θ + sin⁶θ - 1)(tan²θ + cot²θ + 2) + 3 is equal to:

A. 0

B. 1

C. 2

D. -1

Answer: Option A

Solution(By Examveda Team)

(cos⁶θ + sin⁶θ - 1)(tan²θ + cot²θ + 2) + 3
Put θ = 45°
= (cos⁶45° + sin⁶45° - 1)(tan²45° + cot²45° + 2) + 3
$$\eqalign{ & = \left( {\frac{1}{8} + \frac{1}{8} - 1} \right)\left( {1 + 1 + 2} \right) + 3 \cr & = - \frac{3}{4} \times 4 + 3 \cr & = 0 \cr} $$