If the maximum and minimum values of the determinant 1 + sin 2 x cos 2 x sin 2x sin 2 x 1 + cos 2 x sin 2x sin 2 x cos 2 x 1 + sin 2x are α and β respectively, then α + 2 β is equal to

Step-by-step solution

Given determinant is Δ = 1 + sin 2 x cos 2 x sin 2x sin 2 x 1 + cos 2 x sin 2x sin 2 x cos 2 x 1 + sin 2x Applying the operation C 1 → C 1 + C 2 , we get Δ = 2 cos 2 x sin 2x 2 1 + cos 2 x sin 2x 1 cos 2 x 1 + sin 2x Applying the operations R 2 → R 2 - R 1 and then R 3 → R 3 - R 1 , we get Δ = 2 cos 2 x sin 2x 0 1 0 - 1 0 1 Now, expanding the above determinant along R 2 , we get Δ = - 0 + ( 2 + sin 2x ) - 0 = 2 + sin 2x Since, the maximum value of sin 2x is 1 and minimum value