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cos^3 t = Cos^2 t * Cos t = cos t * (cos 2t + 1)/2 (double angle formula)

so i have (cos t)*(cos 2t)/2 + (cos t)/2.

my book's solution says (cos t)*(cos 2t)/2 = (1/2)(cos (2t+1) + cost (2t-1))... how? I can't think of any formulas that give the above result. can someone please explain?

thanks.