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

Step-by-step solution

We have, sin x cos x cos x cos x sin x cos x cos x cos x sin x = 0 , - π 4 ≤ x ≤ π 4 Apply: R 1 → R 1 - R 2 and R 2 → R 2 - R 3 sin x - cos x cos x - sin x 0 0 sin x - cos x cos x - sin x cos x cos x sin x = 0 ⇒ sin x - cos x 2 1 - 1 0 0 1 - 1 cos x cos x sin x = 0 ⇒ sin x - cos x 2 sin x + 2 cos x = 0 ⇒ sin x = cos x or sin x = - 2 cos x ∴   x = π 4 Since, - π 4 ≤ x ≤ π 4 , we get - 1 ≤ tan x ≤ 1 ⇒ tan x = 1