What is the general solution for cos(2θ)=1+3sin(θ) ?

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

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cos(2θ)=1+3sin(θ)

cos (2 θ) = 1 + 3 sin (θ)

θ = 2 πn, θ = π + 2 πn

Solution steps

cos (2 θ) = 1 + 3 sin (θ)

Subtract

1 + 3 sin (θ)

from both sides

cos (2 θ) - 1 - 3 sin (θ) = 0

Rewrite using trig identities

- 2 sin^{2} (θ) - 3 sin (θ) = 0

Solve by substitution

sin (θ) = - \frac{3}{2}, sin (θ) = 0

sin (θ) = - \frac{3}{2} :

No Solution

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

Combine all the solutions

θ = 2 πn, θ = π + 2 πn

cos (2 x) - cos (x) = - 1, 0 \leq x < 2 π

sin (x) = - \frac{1}{10}

sec^{2} (θ) + sec (θ) = 2, 2 π \leq θ \leq 3 π

6 sec^{2} (x) = 0

3 - 2 cos (x) = 2

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