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Find the period of the function f(x)=sin (pi x / n!) - cos (pi x / n+1!

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Solution: We have ,

$f(x)=sin fracpi xn!-cos fracpi x(n+1)!$

$\ \ sin fracpi xn! ightarrow T_1=(frac2pifracpin!) =2n!\ \ cos fracpi x(n+1)! ightarrow T_2=(frac2pifracpi(n+1)!)=2(n+1)!\ \ Rightarrow hspace1cmT=2(n+1)!$

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Deependra Verma

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