What is the general solution for sin^2(x)-4=0 ?

The general solution for sin^2(x)-4=0 is No Solution for x\in\mathbb{R}

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sin^2(x)-4=0

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

No Solution for x \in R

Solution steps

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

Solve by substitution

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

Let:

sin (x) = u

u^{2} - 4 = 0

u^{2} - 4 = 0 : u = 2, u = - 2

u^{2} - 4 = 0

Move

4

to the right side

u^{2} - 4 = 0

Add

4

to both sides

u^{2} - 4 + 4 = 0 + 4

Simplify

u^{2} = 4

u^{2} = 4

For

x^{2} = f (a)

the solutions are

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

u = 4, u = - 4

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

- 4 = - 2

- 4

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= - 2

u = 2, u = - 2

Substitute back

u = sin (x)

sin (x) = 2, sin (x) = - 2

sin (x) = 2, sin (x) = - 2

sin (x) = 2 :

No Solution

sin (x) = 2

- 1 \leq sin (x) \leq 1

No Solution

sin (x) = - 2 :

No Solution

sin (x) = - 2

- 1 \leq sin (x) \leq 1

No Solution

Combine all the solutions

No Solution for x \in R

tan (a) = \frac{2.8}{9}

cos (2 x) - 9 cos (x) + 5 = 0

u, x = 5 tanh (u)

2 sin (x) - csc (x) = 2

5 cos (θ) - 3 = 0

What is the general solution for sin^2(x)-4=0 ?
The general solution for sin^2(x)-4=0 is No Solution for x\in\mathbb{R}