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

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

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

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

x = \frac{2 πn}{3}

Solution steps

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

Subtract

sin^{2} (3 x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (3 x) = 2, cos (3 x) = 1

cos (3 x) = 2 :

No Solution

cos (3 x) = 1 : x = \frac{2 πn}{3}

Combine all the solutions

x = \frac{2 πn}{3}

sin (2 x) + 3 sin (x) = 0

cos (2 θ) + 10 sin^{2} (θ) = 5

9 sin^{2} (θ) - 4 = 0

sec (x) (2 cos (x) - 2) = 0

2 cos (θ) - 2 = 0

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