Solve cos^2a+siv^2d=1

$$\cos ^ { 2 } a + s i v ^ { 2 } d = 1$$

Solve for d

$$\left\{\begin{matrix}d=\frac{i\left(\cos(2a)-1\right)}{2sv^{2}}\text{, }&v\neq 0\text{ and }s\neq 0\\d\in \mathrm{C}\text{, }&\left(\exists n_{1}\in \mathrm{Z}\text{ : }a=\pi n_{1}\text{ and }s=0\right)\text{ or }\left(\exists n_{1}\in \mathrm{Z}\text{ : }a=\pi n_{1}\text{ and }v=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$siv^{2}d=1-\left(\cos(a)\right)^{2}$$

The equation is in standard form.

$$isv^{2}d=\left(\sin(a)\right)^{2}$$

Divide both sides by isv^{2}.

$$\frac{isv^{2}d}{isv^{2}}=\frac{\left(\sin(a)\right)^{2}}{isv^{2}}$$

Dividing by isv^{2} undoes the multiplication by isv^{2}.

$$d=\frac{\left(\sin(a)\right)^{2}}{isv^{2}}$$

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

$$d=-\frac{i\left(\sin(a)\right)^{2}}{sv^{2}}$$