The number of solutions for the equation sin 3 x cos x + sin 2 x cos 2 x + sin x cos 3 x = 1 in the interval 0 , 2 π is/are

Step-by-step solution

sin 3 x cos x + sin 2 x cos 2 x + sin x cos 3 x = 1 ⇒   sin x cos x sin 2 x + sin x cos x + cos 2 x = 1 ⇒ sin 2 x 2 1 + sin 2 x 2 = 1 ⇒   sin 2 x 2 + sin   2 x = 4 ⇒   sin 2 2 x + 2 sin 2 x - 4 = 0 ⇒   sin 2 x = - 2 ± 4 + 16 2 ⇒   sin 2 x = - 1 ± 5 This is not possible. S i n c e   - 1 ≤ sin 2 x ≤ 1 Hence the given equation has no solution.