Processing Math: Done

From Förberedande kurs i matematik 1

For a fixed value of u, an equality of the form

cosu=cosv

is satisfied by two angles v in the unit circle:

v=u and v=−u

This means that all angles v which satisfy the equality are

v=u+2n and v=−u+2n

where n is an arbitrary integer.

Therefore, the equation

cos5x=cosx+5 

has the solutions

5x=x+5+2n or

5x=−x−5+2n

If we collect x onto one side, we end up with

x=20+21nx=−30+31n  ( n an arbitrary integer).