What is the general solution for 5-sin(θ)=cos(2θ) ?

The general solution for 5-sin(θ)=cos(2θ) is No Solution for θ\in\mathbb{R}

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5-sin(θ)=cos(2θ)

5 - sin (θ) = cos (2 θ)

No Solution for θ \in R

Solution steps

5 - sin (θ) = cos (2 θ)

Subtract

cos (2 θ)

from both sides

5 - sin (θ) - cos (2 θ) = 0

Rewrite using trig identities

4 - sin (θ) + 2 sin^{2} (θ) = 0

Solve by substitution

sin (θ) = \frac{1}{4} + i \frac{31}{4}, sin (θ) = \frac{1}{4} - i \frac{31}{4}

sin (θ) = \frac{1}{4} + i \frac{31}{4} :

No Solution

sin (θ) = \frac{1}{4} - i \frac{31}{4} :

No Solution

Combine all the solutions

No Solution for θ \in R

8 sin (θ) + 43 = 0

x, sin (x) = \frac{3}{2}

tan (α) = 2

sin (2 x + \frac{π}{4}) = \frac{2}{2}

cot (θ) = \frac{2}{3}

What is the general solution for 5-sin(θ)=cos(2θ) ?
The general solution for 5-sin(θ)=cos(2θ) is No Solution for θ\in\mathbb{R}