The number of solutions of the equation sin 3 ⁡ x cos ⁡ x + sin 2 ⁡ x cos 2 ⁡ x + cos 3 ⁡ x sin ⁡ x + 1 = 0 in the interval 0 , 2 π is equal to

Step-by-step solution

The given equation can be written as sin ⁡ x cos ⁡ x sin 2 ⁡ x + cos 2 ⁡ x + sin 2 ⁡ x cos 2 ⁡ x + 1 = 0 Substituting t = sin ⁡ x cos ⁡ x in this equation, we get t 2 + t + 1 = 0 . This equation has no real roots.