The value of 2 sin 2 ⁡ θ + 4 cos ⁡ θ + α sin ⁡ α sin ⁡ θ + cos ⁡ 2 ( α + θ ) is

Step-by-step solution

2 sin 2 ⁡ θ + 2 cos ⁡ θ + α cos ⁡ θ - α - cos ⁡ θ + α + 2 cos 2 ⁡ θ + α - 1 = 2 sin 2 ⁡ θ + 2 cos 2 ⁡ θ - sin 2 ⁡ α - 1 = 2 - 2 sin 2 ⁡ α - 1 = cos 2 ⁡ α - sin 2 ⁡ α