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

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

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sin^2(θ)+cos^2(θ)=2

sin^{2} (θ) + cos^{2} (θ) = 2

No Solution for θ \in R

Solution steps

sin^{2} (θ) + cos^{2} (θ) = 2

Subtract

cos^{2} (θ)

from both sides

sin^{2} (θ) = 2 - cos^{2} (θ)

Square both sides

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

Subtract

(2 - cos^{2} (θ))^{2}

from both sides

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

Apply exponent rule:

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

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

Rewrite using trig identities

- 3 + 2 cos^{2} (θ) = 0

Solve by substitution

cos (θ) = \frac{3}{2}, cos (θ) = - \frac{3}{2}

cos (θ) = \frac{3}{2} :

No Solution

cos (θ) = - \frac{3}{2} :

No Solution

Combine all the solutions

No Solution

Verify solutions by plugging them into the original equation

No Solution for θ \in R

sec (θ) - 4.905 = 0

csc (\frac{x}{2}) = 2

5 tan (b) + 7 = 2 tan (b) + 4

cot (x) = 1, 0 \leq x < 2 π

sin (4 x) cos (6 x) - cos (4 x) sin (6 x) = - 0.75

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