What is the general solution for 2sin^2(x)+sqrt(3)=0 ?

The general solution for 2sin^2(x)+sqrt(3)=0 is No Solution for x\in\mathbb{R}

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Popular >

2sin^2(x)+sqrt(3)=0

Solution

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

Solution

No Solution for x \in R

Solution steps

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

Solve by substitution

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

Let:

sin (x) = u

2 u^{2} + 3 = 0

2 u^{2} + 3 = 0 : u = i \frac{3}{2}, u = - i \frac{3}{2}

2 u^{2} + 3 = 0

Move

3

to the right side

2 u^{2} + 3 = 0

Subtract

3

from both sides

2 u^{2} + 3 - 3 = 0 - 3

Simplify

2 u^{2} = - 3

2 u^{2} = - 3

Divide both sides by

2

2 u^{2} = - 3

Divide both sides by

2

\frac{2 u ^{2}}{2} = \frac{- 3}{2}

Simplify

u^{2} = - \frac{3}{2}

u^{2} = - \frac{3}{2}

For

x^{2} = f (a)

the solutions are

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

u = - \frac{3}{2}, u = - - \frac{3}{2}

Simplify

- \frac{3}{2} : i \frac{3}{2}

- \frac{3}{2}

Apply radical rule:

- a = - 1 a

- \frac{3}{2} = - 1 \frac{3}{2}

= - 1 \frac{3}{2}

Apply imaginary number rule:

- 1 = i

= i \frac{3}{2}

Simplify

- - \frac{3}{2} : - i \frac{3}{2}

- - \frac{3}{2}

Simplify

- \frac{3}{2} : i \frac{3}{2}

- \frac{3}{2}

Apply radical rule:

- a = - 1 a

- \frac{3}{2} = - 1 \frac{3}{2}

= - 1 \frac{3}{2}

Apply imaginary number rule:

- 1 = i

= i \frac{3}{2}

= - i \frac{3}{2}

u = i \frac{3}{2}, u = - i \frac{3}{2}

Substitute back

u = sin (x)

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

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

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

No Solution

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

No Solution

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

No Solution

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

No Solution

Combine all the solutions

No Solution for x \in R

Popular Examples

3tan(x/2)-sqrt(3)=0

3 tan (\frac{x}{2}) - 3 = 0

sin^2(x)=(sqrt(3))/2

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

8cos^2(x)+10cos(x)+3=0

8 cos^{2} (x) + 10 cos (x) + 3 = 0

sin(3x)=1,0<= x<2pi

sin (3 x) = 1, 0 \leq x < 2 π

2/pi =sin(x)

\frac{2}{π} = sin (x)

Frequently Asked Questions (FAQ)

What is the general solution for 2sin^2(x)+sqrt(3)=0 ?
The general solution for 2sin^2(x)+sqrt(3)=0 is No Solution for x\in\mathbb{R}