cos2x2cos3x4cosx1 cos2x1 Solutionwe know that when the base

cos(2x)(2cos(3x)+4cos(x)-1) = cos(2x)(-1)

Solution

we know that when the bases are same then the exponents will be equal

so 2cox (3x) + 4 cos (x)-1= -1

=> 2cox (3x) + 4 cos (x) =0

=>2cox (3x) = -4 cos (x)

=> cos 3x= -2 cos x

=>4 cos³ x- 3 cos x= -2 cos x    [cos 3x= 4 cos³ x- 3 cos x]

=> 4 cos³ x = cos x

=> 4cos² x= 1

=> cos² x= 1/4

=> cos x= 1/2

=> cos x= cos 60⁰

therefore x= 60⁰