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

The general solution for sin^2(x)=3(1-cos(x)) is x=2pin

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

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

x = 2 πn

Solution steps

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

Subtract

3 (1 - cos (x))

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = 1, cos (x) = 2

cos (x) = 1 : x = 2 πn

cos (x) = 2 :

No Solution

Combine all the solutions

x = 2 πn

cos (x) = \frac{1}{10}

u, x = 5 sinh (u)

sin (\frac{π}{2} x) + 1 = 0

3 tan^{2} (x) - tan (x) = 0

sin (2 x) = - \frac{1}{2}, 0 \leq x \leq 2 π

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