What is the general solution for sin^4(x)-sin^2(x)+1=0 ?

The general solution for sin^4(x)-sin^2(x)+1=0 is No Solution for x\in\mathbb{R}

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sin^4(x)-sin^2(x)+1=0

sin^{4} (x) - sin^{2} (x) + 1 = 0

No Solution for x \in R

Solution steps

sin^{4} (x) - sin^{2} (x) + 1 = 0

Solve by substitution

sin (x) = \frac{3}{2} + \frac{1}{2} i, sin (x) = - \frac{3}{2} - \frac{1}{2} i, sin (x) = - \frac{3}{2} + \frac{1}{2} i, sin (x) = \frac{3}{2} - \frac{1}{2} i

sin (x) = \frac{3}{2} + \frac{1}{2} i :

No Solution

sin (x) = - \frac{3}{2} - \frac{1}{2} i :

No Solution

sin (x) = - \frac{3}{2} + \frac{1}{2} i :

No Solution

sin (x) = \frac{3}{2} - \frac{1}{2} i :

No Solution

Combine all the solutions

No Solution for x \in R

tan^{3} (x) - tan^{2} (x) - 3 tan (x) + 3 = 0, tan (x) > 1

sin (2 0^{\circ} - θ) - cos (1 0^{\circ} + 3 θ) = 0

tan (x) = \frac{1}{1}

cos (2 θ) + 3 sin (θ) = 2

0 = 2 sin (2 x) - sin (x)

What is the general solution for sin^4(x)-sin^2(x)+1=0 ?
The general solution for sin^4(x)-sin^2(x)+1=0 is No Solution for x\in\mathbb{R}