Solve the equation sec x Squareroot 2 2 sin x Squareroot 3

Solve the equation (sec x + Squareroot 2 (2 sin x +Squareroot 3)= 0. 0lessthanorequalto x lessthanorequalto 2 pi. (Enter your answers as a comma-separated list. if there is no solution, enter NO SOLUTION.) Solve the equation 2 cos^2 x - 3 cos x + 1 = 0, 0 lessthanorequalto x lessthanorequalto 2 pi. (Enter your answers as a comma-separated list. If there is no solution, enter No solution.) Solve the equation 2 sin x + sin 2x = 0 x = 0, plusminus pi/2, plusminus pi, x = 0, plusminus pi, plusminusn 3pi, ... no solution x = 0, plusminus 2 pi, plusminus 4 pi, ...

Solution

2cos²x - 3cosx +1=0

2cos²x-2cosx - cos x +1=0

2cosx(2cosx-1)-1(cosx-1)=0

(2cosx-1)(cos x-1)=0

cosx=1/2     and cos x=1

x=cos^-1(1/2)    and    x= cos^-11

x= pi/3, 5pi/3            and   x=0

x=0,pi/3,5pi/3