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

The general solution for 6-sin(θ)=cos(2θ) is No Solution for θ\in\mathbb{R}

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6-sin(θ)=cos(2θ)

6 - sin (θ) = cos (2 θ)

No Solution for θ \in R

Solution steps

6 - sin (θ) = cos (2 θ)

Subtract

cos (2 θ)

from both sides

6 - sin (θ) - cos (2 θ) = 0

Rewrite using trig identities

5 - sin (θ) + 2 sin^{2} (θ) = 0

Solve by substitution

sin (θ) = \frac{1}{4} + i \frac{39}{4}, sin (θ) = \frac{1}{4} - i \frac{39}{4}

sin (θ) = \frac{1}{4} + i \frac{39}{4} :

No Solution

sin (θ) = \frac{1}{4} - i \frac{39}{4} :

No Solution

Combine all the solutions

No Solution for θ \in R

sin (x) = - \frac{1}{2}, - π \leq x \leq π

- \frac{10 cos ( θ )}{3} = 10 sin (θ)

11 tan (c) + 6 = 3 tan (c) + 6

sin (x) = \frac{- 11}{11 2}

tan (x) = \frac{43}{45}

What is the general solution for 6-sin(θ)=cos(2θ) ?
The general solution for 6-sin(θ)=cos(2θ) is No Solution for θ\in\mathbb{R}