What is the general solution for (1/2)sin^2(x)=1 ?

The general solution for (1/2)sin^2(x)=1 is No Solution for x\in\mathbb{R}

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(1/2)sin^2(x)=1

(\frac{1}{2}) sin^{2} (x) = 1

No Solution for x \in R

Solution steps

(\frac{1}{2}) sin^{2} (x) = 1

Solve by substitution

\frac{1}{2} sin^{2} (x) = 1

Let:

sin (x) = u

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

\frac{1}{2} u^{2} = 1 : u = 2, u = - 2

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

Multiply both sides by

2

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

Multiply both sides by

2

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

Simplify

u^{2} = 2

u^{2} = 2

For

x^{2} = f (a)

the solutions are

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

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

3 = 4 sin (θ)

- 6 sin (x) = 0

9 csc^{2} (x) + 4.5 cot (x) = 45

7 tan (x) = 8 sin (x)

2 cos (3 x) - 2 = 0

What is the general solution for (1/2)sin^2(x)=1 ?
The general solution for (1/2)sin^2(x)=1 is No Solution for x\in\mathbb{R}