Solve sinx+cotxcosx=1/f(x)

$$\sin x + \cot x \cos x = \frac { 1 } { f ( x ) }$$

Solve for f

$$f=\frac{\sin(x)}{x}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}$$

Steps for Solving Linear Equation

Variable f cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by fx.

$$fx\sin(x)+\cot(x)\cos(x)fx=1$$

Combine all terms containing f.

$$\left(x\sin(x)+\cot(x)\cos(x)x\right)f=1$$

The equation is in standard form.

$$\left(x\cos(x)\cot(x)+x\sin(x)\right)f=1$$

Divide both sides by x\sin(x)+\cot(x)\cos(x)x.

$$\frac{\left(x\cos(x)\cot(x)+x\sin(x)\right)f}{x\cos(x)\cot(x)+x\sin(x)}=\frac{1}{x\cos(x)\cot(x)+x\sin(x)}$$

Dividing by x\sin(x)+\cot(x)\cos(x)x undoes the multiplication by x\sin(x)+\cot(x)\cos(x)x.

$$f=\frac{1}{x\cos(x)\cot(x)+x\sin(x)}$$

Divide 1 by x\sin(x)+\cot(x)\cos(x)x.

$$f=\frac{\sin(x)}{x}$$

Variable f cannot be equal to 0.

$$f=\frac{\sin(x)}{x}\text{, }f\neq 0$$