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

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

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

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

x = 2 πn

Solution steps

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

Subtract

sin^{2} (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

cos (x) = 2 :

No Solution

cos (x) = 1 : x = 2 πn

Combine all the solutions

x = 2 πn

2 cos^{2} (θ) + 5 cos (θ) - 2 = - 4

tan (x) = \frac{2}{4}

7 cos (x) + 12 = 6 cos (x) + 13

sin (\frac{x}{2}) + cos (\frac{x}{2}) = 2

cos (θ) = - \frac{1}{2}, 0 \leq θ < 2 π

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