What is the general solution for 9(1-cos(θ))=sin^2(θ) ?

The general solution for 9(1-cos(θ))=sin^2(θ) is θ=2pin

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9(1-cos(θ))=sin^2(θ)

9 (1 - cos (θ)) = sin^{2} (θ)

θ = 2 πn

Solution steps

9 (1 - cos (θ)) = sin^{2} (θ)

Subtract

sin^{2} (θ)

from both sides

9 (1 - cos (θ)) - sin^{2} (θ) = 0

Rewrite using trig identities

8 + cos^{2} (θ) - 9 cos (θ) = 0

Solve by substitution

cos (θ) = 8, cos (θ) = 1

cos (θ) = 8 :

No Solution

cos (θ) = 1 : θ = 2 πn

Combine all the solutions

θ = 2 πn

x, 1 = sin (x)

4 tan (x) sin (x) = - 5 sin (x)

9 cot^{2} (θ) - 4 = 0

4 sin^{2} (θ) = 1 + 4 cos (θ)

4 sin (θ) + 1 = 2 sin (θ)

What is the general solution for 9(1-cos(θ))=sin^2(θ) ?
The general solution for 9(1-cos(θ))=sin^2(θ) is θ=2pin