Solve cosθsqrt{x}=1

$$\cos \theta \sqrt { x } = 1$$

Solve for x

$$x=\frac{1}{\left(\cos(\theta )\right)^{2}}$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }\left(\theta >2\pi n_{1}+\frac{3\pi }{2}\text{ and }\theta <2\pi n_{1}+\frac{5\pi }{2}\right)$$

Steps for Solving Radical Equations

Divide both sides by \cos(\theta ).

$$\frac{\cos(\theta )\sqrt{x}}{\cos(\theta )}=\frac{1}{\cos(\theta )}$$

Dividing by \cos(\theta ) undoes the multiplication by \cos(\theta ).

$$\sqrt{x}=\frac{1}{\cos(\theta )}$$

Square both sides of the equation.

$$x=\frac{1}{\left(\cos(\theta )\right)^{2}}$$

Solve for θ

$$\theta =-\arccos(\frac{1}{\sqrt{x}})+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}$$

$$\theta =\arccos(\frac{1}{\sqrt{x}})+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{, }x\geq 1\text{ and }\frac{1}{\sqrt{x}}\leq 1$$