What is the general solution for sin^2(a)=2sin^2(a)+3 ?

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

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Popular >

sin^2(a)=2sin^2(a)+3

Solution

sin^{2} (a) = 2 sin^{2} (a) + 3

Solution

No Solution for a \in R

Solution steps

sin^{2} (a) = 2 sin^{2} (a) + 3

Solve by substitution

sin^{2} (a) = 2 sin^{2} (a) + 3

Let:

sin (a) = u

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

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

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

Move

2 u^{2}

to the left side

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

Subtract

2 u^{2}

from both sides

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

Simplify

- u^{2} = 3

- u^{2} = 3

Divide both sides by

- 1

- u^{2} = 3

Divide both sides by

- 1

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

Simplify

u^{2} = - 3

u^{2} = - 3

For

x^{2} = f (a)

the solutions are

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

u = - 3, u = - - 3

Simplify

- 3 : 3 i

- 3

Apply radical rule:

- a = - 1 a

- 3 = - 1 3

= - 1 3

Apply imaginary number rule:

- 1 = i

= 3 i

Simplify

- - 3 : - 3 i

- - 3

Simplify

- 3 : 3 i

- 3

Apply radical rule:

- a = - 1 a

- 3 = - 1 3

= - 1 3

Apply imaginary number rule:

- 1 = i

= 3 i

= - 3 i

u = 3 i, u = - 3 i

Substitute back

u = sin (a)

sin (a) = 3 i, sin (a) = - 3 i

sin (a) = 3 i, sin (a) = - 3 i

sin (a) = 3 i :

No Solution

sin (a) = 3 i

No Solution

sin (a) = - 3 i :

No Solution

sin (a) = - 3 i

No Solution

Combine all the solutions

No Solution for a \in R

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Frequently Asked Questions (FAQ)

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