What is the general solution for 2sin^2(x)=3(1-cos(x)) ?

The general solution for 2sin^2(x)=3(1-cos(x)) is x= pi/3+2pin,x=(5pi)/3+2pin,x=2pin

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2sin^2(x)=3(1-cos(x))

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

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

Solution steps

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

Subtract

3 (1 - cos (x))

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

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

cos (x) = 1 : x = 2 πn

Combine all the solutions

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

cos (x) = 0, 72

θ, cos (θ) = \frac{1}{2}

csc (θ) = 2.8

cos (x) = - \frac{2}{5}

2 sec (x) - 7 = 0

What is the general solution for 2sin^2(x)=3(1-cos(x)) ?
The general solution for 2sin^2(x)=3(1-cos(x)) is x= pi/3+2pin,x=(5pi)/3+2pin,x=2pin