What is the general solution for sin^2(x)=sqrt(3) ?

The general solution for sin^2(x)=sqrt(3) 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 >

sin^2(x)=sqrt(3)

sin^{2} (x) = 3

No Solution for x \in R

Solution steps

sin^{2} (x) = 3

Solve by substitution

sin^{2} (x) = 3

Let:

sin (x) = u

u^{2} = 3

u^{2} = 3

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

u = 3, u = - 3

3

Apply radical rule:

a = a^{\frac{1}{2}}

= (3^{\frac{1}{2}})^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 3^{\frac{1}{2} \cdot \frac{1}{2}}

\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}

\frac{1}{2} \cdot \frac{1}{2}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{2 \cdot 2}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{1}{4}

= 3^{\frac{1}{4}}

- 3

Simplify

3

Apply radical rule:

a = a^{\frac{1}{2}}

= (3^{\frac{1}{2}})^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 3^{\frac{1}{2} \cdot \frac{1}{2}}

\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}

\frac{1}{2} \cdot \frac{1}{2}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{2 \cdot 2}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{1}{4}

= 3^{\frac{1}{4}}

Substitute back

u = sin (x)

No Solution

- 1 \leq sin (x) \leq 1

No Solution

No Solution

- 1 \leq sin (x) \leq 1

No Solution

Combine all the solutions

No Solution for x \in R

x, c^{2} = a^{2} + b^{2} - 2 ab \cdot cos (x)

sin (- \frac{π}{8} c) = - \frac{14}{14}

\frac{25}{sin ( x )} = \frac{18}{sin ( 3 6 ^{\circ} )}

7 tan (3 x) - 21 tan (x) = 0

cos (A) = - \frac{3}{25}

What is the general solution for sin^2(x)=sqrt(3) ?
The general solution for sin^2(x)=sqrt(3) is No Solution for x\in\mathbb{R}