Solve operatorname{lom}(x-pi/2)=cosx

$$\operatorname { lom } ( x - \frac { \pi } { 2 } ) = \cos x$$

Solve for l (complex solution)

$$\left\{\begin{matrix}l=\frac{2\cos(x)}{mo\left(2x-\pi \right)}\text{, }&x\neq \frac{\pi }{2}\text{ and }m\neq 0\text{ and }o\neq 0\\l\in \mathrm{C}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}\text{ or }x=\frac{\pi }{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2lom\left(x-\frac{\pi }{2}\right)=2\cos(x)$$

Use the distributive property to multiply 2lom by x-\frac{\pi }{2}.

$$2lomx+2lom\left(-\frac{\pi }{2}\right)=2\cos(x)$$

Express 2\left(-\frac{\pi }{2}\right) as a single fraction.

$$2lomx+\frac{-2\pi }{2}lom=2\cos(x)$$

Cancel out 2 and 2.

$$2lomx-\pi lom=2\cos(x)$$

Combine all terms containing l.

$$\left(2omx-\pi om\right)l=2\cos(x)$$

The equation is in standard form.

$$\left(2mox-\pi mo\right)l=2\cos(x)$$

Divide both sides by 2mox-mo\pi .

$$\frac{\left(2mox-\pi mo\right)l}{2mox-\pi mo}=\frac{2\cos(x)}{2mox-\pi mo}$$

Dividing by 2mox-mo\pi undoes the multiplication by 2mox-mo\pi .

$$l=\frac{2\cos(x)}{2mox-\pi mo}$$

Divide 2\cos(x) by 2mox-mo\pi .

$$l=\frac{2\cos(x)}{mo\left(2x-\pi \right)}$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{2\cos(x)}{lo\left(2x-\pi \right)}\text{, }&x\neq \frac{\pi }{2}\text{ and }o\neq 0\text{ and }l\neq 0\\m\in \mathrm{C}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}\text{ or }x=\frac{\pi }{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2lom\left(x-\frac{\pi }{2}\right)=2\cos(x)$$

Use the distributive property to multiply 2lom by x-\frac{\pi }{2}.

$$2lomx+2lom\left(-\frac{\pi }{2}\right)=2\cos(x)$$

Express 2\left(-\frac{\pi }{2}\right) as a single fraction.

$$2lomx+\frac{-2\pi }{2}lom=2\cos(x)$$

Cancel out 2 and 2.

$$2lomx-\pi lom=2\cos(x)$$

Combine all terms containing m.

$$\left(2lox-\pi lo\right)m=2\cos(x)$$

Divide both sides by 2olx-ol\pi .

$$\frac{\left(2lox-\pi lo\right)m}{2lox-\pi lo}=\frac{2\cos(x)}{2lox-\pi lo}$$

Dividing by 2olx-ol\pi undoes the multiplication by 2olx-ol\pi .

$$m=\frac{2\cos(x)}{2lox-\pi lo}$$

Divide 2\cos(x) by 2olx-ol\pi .

$$m=\frac{2\cos(x)}{lo\left(2x-\pi \right)}$$

Solve for l

$$\left\{\begin{matrix}l=\frac{2\cos(x)}{mo\left(2x-\pi \right)}\text{, }&x\neq \frac{\pi }{2}\text{ and }m\neq 0\text{ and }o\neq 0\\l\in \mathrm{R}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}\text{ or }x=\frac{\pi }{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2lom\left(x-\frac{\pi }{2}\right)=2\cos(x)$$

Use the distributive property to multiply 2lom by x-\frac{\pi }{2}.

$$2lomx+2lom\left(-\frac{\pi }{2}\right)=2\cos(x)$$

Express 2\left(-\frac{\pi }{2}\right) as a single fraction.

$$2lomx+\frac{-2\pi }{2}lom=2\cos(x)$$

Cancel out 2 and 2.

$$2lomx-\pi lom=2\cos(x)$$

Combine all terms containing l.

$$\left(2omx-\pi om\right)l=2\cos(x)$$

The equation is in standard form.

$$\left(2mox-\pi mo\right)l=2\cos(x)$$

Divide both sides by 2omx-\pi om.

$$\frac{\left(2mox-\pi mo\right)l}{2mox-\pi mo}=\frac{2\cos(x)}{2mox-\pi mo}$$

Dividing by 2omx-\pi om undoes the multiplication by 2omx-\pi om.

$$l=\frac{2\cos(x)}{2mox-\pi mo}$$

Divide 2\cos(x) by 2omx-\pi om.

$$l=\frac{2\cos(x)}{mo\left(2x-\pi \right)}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{2\cos(x)}{lo\left(2x-\pi \right)}\text{, }&x\neq \frac{\pi }{2}\text{ and }l\neq 0\text{ and }o\neq 0\\m\in \mathrm{R}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}\text{ or }x=\frac{\pi }{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2lom\left(x-\frac{\pi }{2}\right)=2\cos(x)$$

Use the distributive property to multiply 2lom by x-\frac{\pi }{2}.

$$2lomx+2lom\left(-\frac{\pi }{2}\right)=2\cos(x)$$

Express 2\left(-\frac{\pi }{2}\right) as a single fraction.

$$2lomx+\frac{-2\pi }{2}lom=2\cos(x)$$

Cancel out 2 and 2.

$$2lomx-\pi lom=2\cos(x)$$

Combine all terms containing m.

$$\left(2lox-\pi lo\right)m=2\cos(x)$$

Divide both sides by 2lox-\pi lo.

$$\frac{\left(2lox-\pi lo\right)m}{2lox-\pi lo}=\frac{2\cos(x)}{2lox-\pi lo}$$

Dividing by 2lox-\pi lo undoes the multiplication by 2lox-\pi lo.

$$m=\frac{2\cos(x)}{2lox-\pi lo}$$

Divide 2\cos(x) by 2lox-\pi lo.

$$m=\frac{2\cos(x)}{lo\left(2x-\pi \right)}$$