What is the general solution for sin^2(θ)=5(cos(θ)+1) ?

The general solution for sin^2(θ)=5(cos(θ)+1) is θ=pi+2pin

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sin^2(θ)=5(cos(θ)+1)

sin^{2} (θ) = 5 (cos (θ) + 1)

θ = π + 2 πn

Solution steps

sin^{2} (θ) = 5 (cos (θ) + 1)

Subtract

5 (cos (θ) + 1)

from both sides

sin^{2} (θ) - 5 (cos (θ) + 1) = 0

Rewrite using trig identities

- 4 - cos^{2} (θ) - 5 cos (θ) = 0

Solve by substitution

cos (θ) = - 4, cos (θ) = - 1

cos (θ) = - 4 :

No Solution

cos (θ) = - 1 : θ = π + 2 πn

Combine all the solutions

θ = π + 2 πn

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

cos^{2} (x) = sin^{2} (x)

sin (x + \frac{π}{4}) + sin (x - \frac{π}{4}) = - 1

cos (\frac{x}{4}) = 0

cos (θ) = 0.92

What is the general solution for sin^2(θ)=5(cos(θ)+1) ?
The general solution for sin^2(θ)=5(cos(θ)+1) is θ=pi+2pin