Question

Which value of x does not satisfy the equation sin^2x + sin x = 0

Answer 1

Answer:

$x \neq 0 \pm \pi \cdot i, \forall i \in \mathbb{N}_{O}$ and $x \neq \frac{3\pi}{2}\pm 2\pi \cdot j, \forall j \in \mathbb{N}_{O}$.

Step-by-step explanation:

The equation can be simplified with the help of trigonometric identities:

$\sin x \cdot (\sin x + 1) = 0$

Which means that equation is equal to zero if any component of the product is zero. The solutions of the expression are:

a) $\sin x$

$x = 0 \pm \pi\cdot i,\forall i \in \mathbb{N}_{O}$

b) $\sin x + 1$

$\sin x + 1 = 0$

$\sin x = -1$

$x = \frac{3\pi}{2} \pm 2\pi\cdot i,\forall i \in \mathbb{N}_{O}$

Any value different of both subsets do not satisfy the equation described above.