Example SEQ.T.3. : Suppose $4* \tan(2x-1) +1 = 9$. Find $x$.
Solution: Since $ A \ne 0$ and $B=2, C=1$, the equation can
be solved with
$2x-1 =\arctan \frac D A$ where $A=4,B=2,$ and $D=9$.
So the key solution is $ x =\frac 12(\arctan( \frac 8{4})+1) =\frac
12( \arctan (2)+1) \approx 1.05$
The GeoGebra mapping diagram visualizes the steps in the algebra for
solving equations of the form $f(x)=A*trig(Bx-C)+k=D$ with $A,B \ne 0$ and $trig = \sin, \cos$ or $\tan$.
Comments: You can use the sliders to investigate other examples by $A,B,C$ as well as $k$.
You can move the (red) point
labelled D on the right axis of the mapping diagram to change the value of $D$.