Solve (x)=5tanx-3sinx+4.3r

$$( x ) = 5 \tan x - 3 \sin x + 4.3 r$$

Solve for r

$$r=\frac{5\left(2x\cos(x)+3\sin(2x)-10\sin(x)\right)}{43\cos(x)}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$5\tan(x)-3\sin(x)+4.3r=x$$

Subtract 5\tan(x)-3\sin(x) from both sides.

$$4.3r=x-\left(5\tan(x)-3\sin(x)\right)$$

To find the opposite of 5\tan(x)-3\sin(x), find the opposite of each term.

$$4.3r=x-5\tan(x)+3\sin(x)$$

The equation is in standard form.

$$4.3r=3\sin(x)-5\tan(x)+x$$

Divide both sides of the equation by 4.3, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{4.3r}{4.3}=\frac{\sin(x)\left(-\frac{5}{\cos(x)}+3\right)+x}{4.3}$$

Dividing by 4.3 undoes the multiplication by 4.3.

$$r=\frac{\sin(x)\left(-\frac{5}{\cos(x)}+3\right)+x}{4.3}$$

Divide x+\sin(x)\left(3-\frac{5}{\cos(x)}\right) by 4.3 by multiplying x+\sin(x)\left(3-\frac{5}{\cos(x)}\right) by the reciprocal of 4.3.

$$r=\frac{10\left(\sin(x)\left(-\frac{5}{\cos(x)}+3\right)+x\right)}{43}$$