What is the general solution for sin^2(θ)=8-2cos^2(θ) ?

The general solution for sin^2(θ)=8-2cos^2(θ) is No Solution for θ\in\mathbb{R}

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sin^2(θ)=8-2cos^2(θ)

sin^{2} (θ) = 8 - 2 cos^{2} (θ)

No Solution for θ \in R

Solution steps

sin^{2} (θ) = 8 - 2 cos^{2} (θ)

Subtract

8 - 2 cos^{2} (θ)

from both sides

sin^{2} (θ) - 8 + 2 cos^{2} (θ) = 0

Rewrite using trig identities

- 6 - sin^{2} (θ) = 0

Solve by substitution

sin (θ) = 6 i, sin (θ) = - 6 i

sin (θ) = 6 i :

No Solution

sin (θ) = - 6 i :

No Solution

Combine all the solutions

No Solution for θ \in R

10 sin (x) + 16 = 3 sin (x) + 9

2 sin (5 θ) = 0

x, sin^{2} (x) = 1

tan^{4} (x) - 2 = tan^{2} (x) + sec^{2} (x)

cos (x - \frac{π}{4}) = - sin (x)

What is the general solution for sin^2(θ)=8-2cos^2(θ) ?
The general solution for sin^2(θ)=8-2cos^2(θ) is No Solution for θ\in\mathbb{R}