If f x = sin 2 ⁡ x + sin 2 ⁡ x + π 3 + cos ⁡ x cos ⁡ x + π 3 and g 5 4 = 1 , then g o f ( x ) is equal to

Step-by-step solution

Given, f x = sin 2 ⁡ x + sin 2 ⁡ x + π 3 + cos ⁡ x cos ⁡ x + π 3 = sin 2 ⁡ x + sin ⁡ x cos ⁡ π 3 + cos ⁡ x sin ⁡ π 3 2 + cos ⁡ x cos ⁡ x cos ⁡ π 3 - sin ⁡ x sin ⁡ π 3 = sin 2 ⁡ x + sin ⁡ x 2 + cos ⁡ x . 3 2 2 + cos ⁡ x cos ⁡ x 2 - sin ⁡ x . 3 2 = sin 2 ⁡ x + sin 2 ⁡ x 4 + 3 cos 2 ⁡ x 4 + sin ⁡ x cos ⁡ x .   3 2 + cos 2 ⁡ x 2 -