The number of distinct real roots of the equation, cos x sin x sin x sin x cos x sin x sin x sin x cos x = 0 in the interval - π 4 , π 4 is :

Step-by-step solution

Given equation cos x sin x sin x sin x cos x sin x sin x sin x cos x = 0 Performing row and column operations R 1 → R 1 - R 2 R 2 → R 2 - R 3 ⇒ cos x - sin x sin x - cos x 0 0 cos x - sin x sin x - cos x sin x sin x cos x = 0 C 2 → C 2 + C 3 ⇒ cos x - sin x sin x - cos x 0 0 0 sin x - cos x sin x sin x + cos x cos x = 0 Expanding using second row, we get sin x + cos x cos x - sin x - sin x sin x - cos x = 0 ⇒ cos x - sin x sin x + cos x + sin x = 0 ⇒ cos x - sin x 2 sin x +