Question

The number of solutions of the equation \(cos \bigg(x+\frac{π}{3}\bigg)cos\bigg(\frac{π}{3-x}\bigg)=\frac{1}{4}cos^22x,x ∈ [-3π, 3π]\) is:

• A. 8
• B. 5
• C. 6
• D. 7

Answer 1

The Correct Option is D

\(cos \bigg(x+\frac{π}{3}\bigg)cos\bigg(\frac{π}{3-x}\bigg)=\frac{1}{4}cos^22x,x ∈ [-3π, 3π]\)

\(⇒ cos2x + cos \frac{2π}{3} = \frac{1}{2} cos^22x\)

\(⇒ cos^22x - 2cos^2x - 1 = 0\)

\(⇒ cos2x = 1\)

Therefore,  x can have  \(-3π, -2π, -π,0,π,2π,3π\)  [Seven different results]

Hence, the correct option is (D): \(7\)