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

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

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sin^2(θ)-2=cos^2(θ)

sin^{2} (θ) - 2 = cos^{2} (θ)

No Solution for θ \in R

Solution steps

sin^{2} (θ) - 2 = cos^{2} (θ)

Subtract

cos^{2} (θ)

from both sides

sin^{2} (θ) - 2 - cos^{2} (θ) = 0

Rewrite using trig identities

sin^{2} (θ) - 2 - cos^{2} (θ)

Use the Double Angle identity:

cos^{2} (x) - sin^{2} (x) = cos (2 x)

- cos^{2} (x) + sin^{2} (x) = - cos (2 x)

= - 2 - cos (2 θ)

- 2 - cos (2 θ) = 0

Move

2

to the right side

- 2 - cos (2 θ) = 0

Add

2

to both sides

- 2 - cos (2 θ) + 2 = 0 + 2

Simplify

- cos (2 θ) = 2

- cos (2 θ) = 2

Divide both sides by

- 1

- cos (2 θ) = 2

Divide both sides by

- 1

\frac{- cos ( 2 θ )}{- 1} = \frac{2}{- 1}

Simplify

cos (2 θ) = - 2

cos (2 θ) = - 2

- 1 \leq cos (x) \leq 1

No Solution for θ \in R

cos (x) = 0, 88

21 = 24 + 8 cos (\frac{π t}{6})

cos (\frac{5}{2} x) = 0

sin (5 x) = sin (7 x)

cos (x) = 0, 60

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