Let A = 1 3 cos ⁡ 2 θ 1 sin ⁡ 2 θ 1 3 cos ⁡ 2 θ 1 sin ⁡ 2 θ 1 . If the maximum value of A is equal to k , then k - 3 2 is equal to

Step-by-step solution

A = 1 1 - 3 sin ⁡ 2 θ cos ⁡ 2 θ - 3 cos ⁡ 2 θ sin ⁡ 2 θ - 3 cos ⁡ 2 θ + 1 sin 2 ⁡ 2 θ - 1 = 1 - 3 sin ⁡ 4 θ + 9 cos 2 ⁡ 2 θ + sin 2 ⁡ 2 θ - 1 = 1 - 3 sin ⁡ 4 θ + 1 + 8 cos 2 ⁡ 2 θ - 1 = 1 - 3 sin ⁡ 4 θ + 4 + 4 cos ⁡ 4 θ A = 5 - 3 sin ⁡ 4 θ + 4 cos ⁡ 4 θ A m a x = 10