JEE Main202429 Jan 2024Evening ShiftMathematicsTrigonometric EquationsActual
The sum of the solutions x ∈ R of the equation 3 cos 2 x + cos 3 2 x cos 6 x - sin 6 x = x 3 - x 2 + 6 is
Options
- A0
- B1
- C- 1
- D3
Correct answer
C. - 1
Step-by-step solution
Given: 3 cos 2 x + cos 3 2 x cos 6 x - sin 6 x = x 3 - x 2 + 6 ⇒ cos 2 x 3 + cos 2 2 x cos 2 x 3 - sin 2 x 3 = x 3 - x 2 + 6 ⇒ cos 2 x 3 + cos 2 2 x cos 2 x - sin 2 x cos 4 x + sin 4 x + sin 2 x cos 2 x = x 3 - x 2 + 6 ⇒ 3 + cos 2 2 x sin 2 x + cos 2 x 2 - 2 sin 2 x cos 2 x + sin 2 x cos 2 x = x 3 - x 2 + 6 ⇒ 3 + cos 2 2 x 1 - sin 2 x cos 2 x = x 3 - x 2 + 6 ⇒ 3 + cos 2 2 x 1 - 2 sin x cos x 2 4 = x 3 - x 2 + 6 ⇒ 4 3 + cos 2 2 x 4 - sin 2 2 x = x 3 - x 2 + 6 ⇒ 4 3 + 1 - sin 2 2 x 4 - sin 2 2 x = x 3 - x 2 + 6 ⇒ 4 =