Lösung 4.4:6a
Aus Online Mathematik Brückenkurs 1
If we move everything over to the left-hand side,
we see that both terms have \displaystyle \sin x as a common factor which we can take out,
In this factorized version of the equation, we see the equation has a solution only when one of the factors \displaystyle \sin x or \displaystyle \cos 3x-2 is zero. The factor \displaystyle \sin x is zero for all values of x that are given by
(see exercise 3.5:2c). The other factor \displaystyle \cos 3x-2 can never be zero because the value of a cosine always lies between \displaystyle -1 and \displaystyle 1, which gives that the largest value of \displaystyle \cos 3x-2 is \displaystyle -1.
The solutions are therefore
