What is the general solution for 8(1-cos(θ))=sin^2(θ) ?

The general solution for 8(1-cos(θ))=sin^2(θ) is θ=2pin

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8(1-cos(θ))=sin^2(θ)

8 (1 - cos (θ)) = sin^{2} (θ)

θ = 2 πn

Solution steps

8 (1 - cos (θ)) = sin^{2} (θ)

Subtract

sin^{2} (θ)

from both sides

8 (1 - cos (θ)) - sin^{2} (θ) = 0

Rewrite using trig identities

7 + cos^{2} (θ) - 8 cos (θ) = 0

Solve by substitution

cos (θ) = 7, cos (θ) = 1

cos (θ) = 7 :

No Solution

cos (θ) = 1 : θ = 2 πn

Combine all the solutions

θ = 2 πn

x, cos (x) = sin (x)

cos (2 θ) - cos (θ) = - 1

- 6 cos (θ) + 4 = 4

4 cos (x) = - sin^{2} (x) + 4

7 cos^{2} (θ) + 5 = 2 sin (θ) + 7

What is the general solution for 8(1-cos(θ))=sin^2(θ) ?
The general solution for 8(1-cos(θ))=sin^2(θ) is θ=2pin