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## Answers

f(x+m) = f(x) for all m>0

tan(π+x) = tanx

hence tanx is periodic with period π not 2π.

A function f is said to be periodic with period m, if we have

f (x + m) = f (x), For every m > 0.

It means that the function f(x) possess same values after an interval of "m". One can say that the function f repeats all its values after every interval of "m".

For example - The sine function i.e. sin x has a period 2 π because 2 π is the smallest number for which sin (x + 2π) = sin x, for all x.

We may also calculate the period using the formula derived from the basic sine and cosine equations. The period for function y = A sin( B x - c ) and y = A cos( B x - c ) is 2πB radians. The reciprocal of period of a function is equal to its frequency. Frequency is defined as the number of cycles completed in one second. If the period of a function is denoted by P and f be its frequency, then -

f = 1P.