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Answer 1 · 2017-04-06T12:35:09

Use the sum-to-product formula for cosine

The sum-to-product formula for cosine states:

#cos(A) + cos(B) = 2cos((A+B)/2)cos((A-B)/2)#

Specifically, that gives

#cos(5x) + cos(3x) = cos(4x)cos(x)#

Therefore the equation is equivalent to

#cos(4x)cos(x) = cos(x)#

This equation has solutions when cosx = 0 or when

cos(4x) = 1.

Solve these much simpler equations, and you're done.