Lösung 4.4:8a
Aus Online Mathematik Brückenkurs 1
If we use the formula for double angles, \displaystyle \sin 2x = 2\sin x\cos x, and move all the terms over to the left-hand side, the equation becomes
Then, we see that we can take a factor \displaystyle \cos x out of both terms,
and hence divide up the equation into two cases. The equation is satisfied either if \displaystyle \cos x = 0 or if \displaystyle 2\sin x-\sqrt{2} = 0\,.
\displaystyle \cos x = 0:
This equation has the general solution
\displaystyle 2\sin x-\sqrt{2}=0:
If we collect \displaystyle \sin x on the left-hand side, we obtain the equation \displaystyle \sin x = 1/\!\sqrt{2}, which has the general solution
where n is an arbitrary integer.
The complete solution of the equation is
where n is an arbitrary integer.
