Solve xsin^2alpha+cos^2alpha=1

$$x \sin ^ { 2 } \alpha + \cos ^ { 2 } \alpha = 1$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{\cos(2\alpha )-1}{2\left(\sin(\alpha )\right)^{2}}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\alpha =\pi n_{1}\\x\in \mathrm{C}\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }\alpha =\pi n_{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \left(\cos(\alpha )\right)^{2} from both sides.

$$x\left(\sin(\alpha )\right)^{2}=1-\left(\cos(\alpha )\right)^{2}$$

The equation is in standard form.

$$\left(\sin(\alpha )\right)^{2}x=\left(\sin(\alpha )\right)^{2}$$

Divide both sides by \left(\sin(\alpha )\right)^{2}.

$$\frac{\left(\sin(\alpha )\right)^{2}x}{\left(\sin(\alpha )\right)^{2}}=\frac{\left(\sin(\alpha )\right)^{2}}{\left(\sin(\alpha )\right)^{2}}$$

Dividing by \left(\sin(\alpha )\right)^{2} undoes the multiplication by \left(\sin(\alpha )\right)^{2}.

$$x=\frac{\left(\sin(\alpha )\right)^{2}}{\left(\sin(\alpha )\right)^{2}}$$

Divide \left(\sin(\alpha )\right)^{2} by \left(\sin(\alpha )\right)^{2}.

$$x=1$$

Solve for x

$$\left\{\begin{matrix}\\x=1\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }\alpha =\pi n_{1}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \left(\cos(\alpha )\right)^{2} from both sides.

$$x\left(\sin(\alpha )\right)^{2}=1-\left(\cos(\alpha )\right)^{2}$$

The equation is in standard form.

$$\left(\sin(\alpha )\right)^{2}x=-\left(\cos(\alpha )\right)^{2}+1$$

Divide both sides by \left(\sin(\alpha )\right)^{2}.

$$\frac{\left(\sin(\alpha )\right)^{2}x}{\left(\sin(\alpha )\right)^{2}}=\frac{\left(\sin(\alpha )\right)^{2}}{\left(\sin(\alpha )\right)^{2}}$$

Dividing by \left(\sin(\alpha )\right)^{2} undoes the multiplication by \left(\sin(\alpha )\right)^{2}.

$$x=\frac{\left(\sin(\alpha )\right)^{2}}{\left(\sin(\alpha )\right)^{2}}$$

Divide \left(\sin(\alpha )\right)^{2} by \left(\sin(\alpha )\right)^{2}.

$$x=1$$

Solve for α (complex solution)

$$\left\{\begin{matrix}\\\alpha =\pi n_{1}\text{, }n_{1}\in \mathrm{Z}\text{, }&\text{unconditionally}\\\alpha \in \mathrm{C}\text{, }&x=1\end{matrix}\right.$$

Solve for α

$$\left\{\begin{matrix}\\\alpha =\pi n_{1}\text{, }n_{1}\in \mathrm{Z}\text{, }&\text{unconditionally}\\\alpha \in \mathrm{R}\text{, }&x=1\end{matrix}\right.$$