Let f x = 1 + sin 2 x cos 2 x sin 2 x sin 2 x 1 + cos 2 x sin 2 x sin 2 x cos 2 x 1 + sin 2 x , x ∈ π 6 , π 3 . If α and β respectively are the maximum and the minimum values of f , then

Step-by-step solution

Given: f x = 1 + sin 2 x cos 2 x sin 2 x sin 2 x 1 + cos 2 x sin 2 x sin 2 x cos 2 x 1 + sin 2 x Applying C 1 → C 1 + C 2 + C 3 f x = 2 + sin 2 x cos 2 x sin 2 x 2 + sin 2 x 1 + cos 2 x sin 2 x 2 + sin 2 x cos 2 x 1 + sin 2 x ⇒ f x = 2 + sin 2 x 1 cos 2 x sin 2 x 1 1 + cos 2 x sin 2 x 1 cos 2 x 1 + sin 2 x Applying R 2 → R 2 - R 1 and R 3 → R 3 - R 1 f x = 2 + sin 2 x 1 cos 2 x sin 2 x 0 1 0 0 0 1 ⇒ f x = 2 + sin 2 x 1 = 2 + sin 2 x Now, for x ∈ π 6 , π 3 ⇒ 2 x &#