Solve the trigonometric equation 3 3 sin 2 cos2 Solution3

Solve the trigonometric equation: 3 + 3 sin = 2 cos² .

Solution

3 + 3 sin = 2 cos2

3 + 3sin = 2( 1-2sin^2)

4sin^2 +3sin +1 =0

solve the quadratic equation by quadratice root formula

x= ( -b +/-sqrt(b^2 -4ac))/2a

sin = ( -3 +/- sqrt(9 -16) )/8

since there are no real solutions to the above equation.Therefore no solution exist