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

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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