What is the general solution for sin^2(θ)=6(cos(-θ)+1) ?

The general solution for sin^2(θ)=6(cos(-θ)+1) is θ=pi+2pin

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sin^2(θ)=6(cos(-θ)+1)

sin^{2} (θ) = 6 (cos (- θ) + 1)

θ = π + 2 πn

Solution steps

sin^{2} (θ) = 6 (cos (- θ) + 1)

Rewrite using trig identities

sin^{2} (θ) = 6 (1 + cos (θ))

Subtract

6 (1 + cos (θ))

from both sides

sin^{2} (θ) - 6 (1 + cos (θ)) = 0

Rewrite using trig identities

- 5 - cos^{2} (θ) - 6 cos (θ) = 0

Solve by substitution

cos (θ) = - 5, cos (θ) = - 1

cos (θ) = - 5 :

No Solution

cos (θ) = - 1 : θ = π + 2 πn

Combine all the solutions

θ = π + 2 πn

5 sin (θ) - 2 = 0

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

- 4 cos (5 x) + 1 = 1

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

6 sin^{2} (θ) - 13 sin (θ) + 7 = 0

What is the general solution for sin^2(θ)=6(cos(-θ)+1) ?
The general solution for sin^2(θ)=6(cos(-θ)+1) is θ=pi+2pin