6cos2x3cosx30 Find all the solutions of the equation on the

6cos^2x+3cosx-3=0

Find all the solutions of the equation on the interval [0,2pi)

Solution

6cos²x+3cosx-3=0

=>6cos²x+6cosx-3cosx-3=0

=>6cosx(cosx+1) -3(cosx+1)=0

=>(cosx+1)(6cosx-3)=0

=>cosx +1 =0, 6cosx -3=0

=> cosx =-1 , cosx=1_/2

cosx =-1  => x=

cosx =1_/2  => x=_/3,5_/3

all the solutions of the equation on the interval [0,2pi) are x=_/3,,5_/3