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

The general solution for cos(θ)-2sin^2(θ)=-1 is θ= pi/3+2pin,θ=(5pi)/3+2pin,θ=pi+2pin

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cos(θ)-2sin^2(θ)=-1

cos (θ) - 2 sin^{2} (θ) = - 1

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn, θ = π + 2 πn

Solution steps

cos (θ) - 2 sin^{2} (θ) = - 1

Subtract

- 1

from both sides

cos (θ) - 2 sin^{2} (θ) + 1 = 0

Rewrite using trig identities

- 1 + cos (θ) + 2 cos^{2} (θ) = 0

Solve by substitution

cos (θ) = \frac{1}{2}, cos (θ) = - 1

cos (θ) = \frac{1}{2} : θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

cos (θ) = - 1 : θ = π + 2 πn

Combine all the solutions

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn, θ = π + 2 πn

4 + 4 cos (θ) = 0

- cot (2 θ) = 0

1 - \frac{1}{2} \cdot cos (3 θ) = \frac{4 - 2}{4}, 0^{\circ} \leq θ \leq 36 0^{\circ}

\frac{cos ( x )}{sin ( x )} = - 0.00836

sin^{3} (x) = cos^{3} (x)

What is the general solution for cos(θ)-2sin^2(θ)=-1 ?
The general solution for cos(θ)-2sin^2(θ)=-1 is θ= pi/3+2pin,θ=(5pi)/3+2pin,θ=pi+2pin