What is the general solution for 3-3cos(x)=2sin^2(x) ?

The general solution for 3-3cos(x)=2sin^2(x) is x=2pin,x= pi/3+2pin,x=(5pi)/3+2pin

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3-3cos(x)=2sin^2(x)

3 - 3 cos (x) = 2 sin^{2} (x)

x = 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

3 - 3 cos (x) = 2 sin^{2} (x)

Subtract

2 sin^{2} (x)

from both sides

3 - 3 cos (x) - 2 sin^{2} (x) = 0

Rewrite using trig identities

1 + 2 cos^{2} (x) - 3 cos (x) = 0

Solve by substitution

cos (x) = 1, cos (x) = \frac{1}{2}

cos (x) = 1 : x = 2 πn

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

2 + 3 sin (x) + sin^{2} (x) - cos^{2} (x) = 0

sin (\frac{π x}{4}) = 0

tan^{2} (x) = - 1 - 2 tan (- x)

cos (x) = 0.45

cos (x) = 0.78

What is the general solution for 3-3cos(x)=2sin^2(x) ?
The general solution for 3-3cos(x)=2sin^2(x) is x=2pin,x= pi/3+2pin,x=(5pi)/3+2pin