Solve tan^-1(2sin^2t/2/2sinfrac{t{2}cost/2})=ta

$$\tan ^ { - 1 } ( \frac { 2 \sin ^ { 2 } \frac { t } { 2 } } { 2 \sin \frac { t } { 2 } \cos \frac { t } { 2 } } ) = t a$$

Solve for a

$$a=\frac{\arctan(\tan(\frac{t}{2}))}{t}$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }\left(t>\pi n_{1}\text{ and }t<\pi n_{1}+\pi \right)$$

Steps for Solving Linear Equation

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

$$ta=\arctan(\frac{2\left(\sin(\frac{t}{2})\right)^{2}}{2\sin(\frac{t}{2})\cos(\frac{t}{2})})$$

The equation is in standard form.

$$ta=\arctan(\frac{\sin(\frac{t}{2})}{\cos(\frac{t}{2})})$$

Divide both sides by t.

$$\frac{ta}{t}=\frac{\arctan(\tan(\frac{t}{2}))}{t}$$

Dividing by t undoes the multiplication by t.

$$a=\frac{\arctan(\tan(\frac{t}{2}))}{t}$$