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 sinx 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 sinx or cos3x−2 is zero. The factor sinx is zero for all values of x that are given by

x=n(n is an arbitrary integer)

(see exercise 3.5:2c). The other factor cos3x−2 can never be zero because the value of a cosine always lies between −1 and 1, which gives that the largest value of cos3x−2 is −1.

The solutions are therefore

x=n(n is an arbitrary integer).