Solve #cos^4x-1=0# for all values of x?

Question

Please show your work!

4366 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-16T03:04:43

General solution
#x= 0+2pin#
#x= pi+2pin#
#n# is an element of all integers

#cos^4x-1=0#

#cos^4x=1#

Fourth root both sides (remember for all implemented even roots, the value can be positive or negative):

#cosx= +-root(4)(1)#
#cosx= +-1#

#x= 0 and pi#

General solution
#x= 0+2pin#
#x= pi+2pin#
#n# is an element of all integers