What is the general solution for cos^2(θ)+sin^2(θ)=4 ?

The general solution for cos^2(θ)+sin^2(θ)=4 is No Solution for θ\in\mathbb{R}

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cos^2(θ)+sin^2(θ)=4

cos^{2} (θ) + sin^{2} (θ) = 4

No Solution for θ \in R

Solution steps

cos^{2} (θ) + sin^{2} (θ) = 4

Subtract

sin^{2} (θ)

from both sides

cos^{2} (θ) = 4 - sin^{2} (θ)

Square both sides

(cos^{2} (θ))^{2} = (4 - sin^{2} (θ))^{2}

Subtract

(4 - sin^{2} (θ))^{2}

from both sides

cos^{4} (θ) - 16 + 8 sin^{2} (θ) - sin^{4} (θ) = 0

Apply exponent rule:

a^{b} = a^{2} a^{b - 2}

- 16 - sin^{4} (θ) + 8 sin^{2} (θ) + cos^{2} (θ) cos^{2} (θ) = 0

Rewrite using trig identities

- 15 + 6 sin^{2} (θ) = 0

Solve by substitution

sin (θ) = \frac{5}{2}, sin (θ) = - \frac{5}{2}

sin (θ) = \frac{5}{2} :

No Solution

sin (θ) = - \frac{5}{2} :

No Solution

Combine all the solutions

No Solution

Verify solutions by plugging them into the original equation

No Solution for θ \in R

6 arccos (x) - 3 π = 3 arccos (x)

3 sin (2 x) = sin (x)

cos (b) = \frac{12}{37}

27 (sin (2 t) cos (t) - (sin (t))^{3}) = 0

2 cos^{2} (x) + cos^{2} (x) = 0

What is the general solution for cos^2(θ)+sin^2(θ)=4 ?
The general solution for cos^2(θ)+sin^2(θ)=4 is No Solution for θ\in\mathbb{R}