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

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

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

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

No Solution for x \in R

Solution steps

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

Subtract

sin^{2} (x)

from both sides

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

Square both sides

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

Subtract

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

from both sides

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

Apply exponent rule:

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

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

Rewrite using trig identities

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

Solve by substitution

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

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

No Solution

sin (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

- 5 π sin (\frac{π ( t )}{2}) = 7.071

9.8 \cdot sin (x) - 19.6 \cdot cos (x) = 4.7

cos (x) = - 3 sin (x)

sin (α) = \frac{3}{5}, 0 < a < \frac{π}{2}

- \frac{15 ( 0.5 cos ( x ) - sin ( x ) )}{( 0.5 sin ( x ) + cos ( x ) ) ^{2}} = 0

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