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Given that cos(3x)=acos^3(x)−bcos(x) is a trigonometric identity, what is the value of a+b

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The commonly recognized expansion formula for
cos(3x) =4 cos^3 (x) - 3cos x
matching this with yours would give us
a = 4 and b = -3

so a+b = 4-3 = -1

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