How to solve this trigonometric equation: cos(x) * cos(2x) * cos (3x) = 1? Thank you!

1 Answer
Ananda Dasgupta
Mar 26, 2018

#x=n pi, n in ZZ#

Explanation:

Since #|cos theta| le 1# , the only way the product of three cosines can be one is if either

  • all three are 1
  • two of them are -1, and the third is equal to +1

The first possibility would mean that #x=2npi, n in ZZ#.

The second would happen when #cos x = -1# (this would automatically lead to #cos2x = +1# and #cos 3x=-1#), which corresponds to #x = (2n+1)pi, n in ZZ#.

Combining the rtwo together we get the solution set

#x=n pi, n in ZZ#

Note : in the second case we could not have taken #cos2x=-1# because that would have led to #cos x = 1/2(1+cos2x) = 0#

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