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period is below where function repeats at x = pi divided by 2 it repeats first substitute x is equal to zero you get if x is equal to Cos 1 + 1 and now substitute x is equal to pi by divided by 2 you again get f(x) is equal to cos 1 + 1 therefore pi by 2 is period of f(x).
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HERE'S YOUR ANSWER MATE......
THE PERIOD OF(X = COS(COS X)+ COS(SIN X) IS PI/2.............
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