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

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

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sin^2(x)+cos^2(x)=2

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

No Solution for x \in R

Solution steps

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

Subtract

cos^{2} (x)

from both sides

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

Square both sides

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

Subtract

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

from both sides

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

Apply exponent rule:

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

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

Rewrite using trig identities

- 3 + 2 cos^{2} (x) = 0

Solve by substitution

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

cos (x) = \frac{3}{2} :

No Solution

cos (x) = - \frac{3}{2} :

No Solution

Combine all the solutions

No Solution

Verify solutions by plugging them into the original equation

No Solution for x \in R

cot (\frac{2 θ}{3}) = - 3

- 3 sin (2 θ) = 5 cos (2 θ), 0^{\circ} \leq 2 θ < 72 0^{\circ}

sin (4 x) = 1

2 sin^{2} (x) = 1 - cos (x)

3 cos (x) tan (x) + tan (x) = 0

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