Solve a=2kpi+pi/2quadtana/2=?

$$a = 2 k \pi + \frac { \pi } { 2 } \quad \tan \frac { a } { 2 } = ?$$

Solve for k

$$k=\frac{2a\cos(\frac{a}{2})-\pi \sin(\frac{a}{2})}{4\pi \cos(\frac{a}{2})}$$

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

Steps for Solving Linear Equation

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

$$2k\pi +\frac{\pi }{2}\tan(\frac{a}{2})=a$$

Subtract \frac{\pi }{2}\tan(\frac{a}{2}) from both sides.

$$2k\pi =a-\frac{\pi }{2}\tan(\frac{a}{2})$$

Multiply both sides of the equation by 2.

$$4k\pi =2a-\pi \tan(\frac{a}{2})$$

The equation is in standard form.

$$4\pi k=-\pi \tan(\frac{a}{2})+2a$$

Divide both sides by 4\pi .

$$\frac{4\pi k}{4\pi }=\frac{-\pi \tan(\frac{a}{2})+2a}{4\pi }$$

Dividing by 4\pi undoes the multiplication by 4\pi .

$$k=\frac{-\pi \tan(\frac{a}{2})+2a}{4\pi }$$

Divide 2a-\pi \tan(\frac{a}{2}) by 4\pi .

$$k=\frac{-\tan(\frac{a}{2})+\frac{2a}{\pi }}{4}$$