For x ϵ 0 , π , the equation sin ⁡ x + 2 sin ⁡ 2 x - sin ⁡ 3 x = 3 has

Step-by-step solution

sin ⁡ x + 2 sin ⁡ 2 x - sin ⁡ 3 x = 3 sin ⁡ x + 4 sin ⁡ x cos ⁡ x - 3 sin ⁡ x + 4 sin 3 ⁡ x = 3 sin ⁡ x - 2 + 4 cos ⁡ x + 4 1 - cos 2 ⁡ x = 3 sin ⁡ x 2 - 4 cos 2 ⁡ x - 4 cos ⁡ x + 1 + 1 = 3 sin ⁡ x 3 - 2 cos ⁡ x - 1 2 = 3 ⇒ sin ⁡ x = 1 a n d 2 cos ⁡ x - 1 = 0 ⇒ x = π 2 a n d x = π 3 Which is not possible at same time Hence, no solution