Solution 4.4:5a
From Förberedande kurs i matematik 1
If we consider for a moment the equality
)
where
−u
(The only exception is when
2
2
−u
We obtain all the angles
−u+2n
where
If we now go back to our equation
the reasoning above shows that the equation is only satisfied when
\displaystyle 3x=x+2n\pi
or
\displaystyle 3x=\pi -x+2n\pi
If we make
\displaystyle x
the subject of each equation, we obtain the full solution to the equation:
\displaystyle \left\{ \begin{array}{*{35}l}
x=0+n\pi \\
x=\frac{\pi }{4}+\frac{1}{2}n\pi \\
\end{array} \right.