The sum of the solutions x ∈R of the equation 3 cos ⁡2x+ cos^3 ⁡2x cos^6 ⁡x- sin^6 ⁡x=x^3-x^2+6 is

Question

Accepted Answer

Correct answer: C. (c) 3 cos ⁡2x+ cos^3 ⁡2x cos^6 ⁡x- sin^6 ⁡x=x^3-x^2+6 ⇒ cos ⁡2x(3+ cos^2 ⁡2x) cos ⁡2x(1- sin^2 ⁡x cos^2 ⁡x)=x^3-x^2+6 ⇒ 4(3+ cos^2 ⁡2x)(4- sin^2 ⁡2x)=x^3-x^2+6 ⇒ 4(3+ cos^2 ⁡2x)(3+ cos^2 ⁡2x)=x^3-x^2+6x^3-x^2+2=0 ⇒ (x+1 )(x^2-2x+2)=0 so, sum of real solutions =-1

$The sum of the solutions x \in R of the equation \frac{3 cos 2 x + cos ^{3} 2 x}{cos ^{6} x - sin ^{6} x} = x^{3} - x^{2} + 6 is$

Solution

More Trigonometric Equations PYQs