How to change the form: cos(3x-30°)+cos(3x+60°) into the form: k cos(x-theta)?

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Answer 1 · 2017-10-05T11:38:26

# sqrt2cos(3x+15^@).#

We know that, #cosC+cosD=2cos((C+D)/2)cos((C-D)/2).#

#:. cos(3x-30^@)+cos(3x+60^@),#

#=2cos(3x+15^@)cos45^@,#

#=2*1/sqrt2*cos(3x+15^@),#

#=sqrt2cos(3x+15^@).#

Answer 2 · 2017-10-05T11:46:24

See below.

Due to period difference it is not possible such change. See the attached plot. In red #cos(3x-30^@)+cos(3x+60^@)# and in blue #cos x#

enter image source here