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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

No Solution for x \in R

Solution steps

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

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

sin (x) - 3 cos (x) = 1, 0 \leq x \leq 2 π

arccos (θ) = \frac{5}{7}

cos (θ) = \frac{- 139}{160}

sin (4 x) = \frac{2}{2}

3 cos (x) = 6

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