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if period of function cos(nx).sin(5x/n) is 3 pi, then number of integral values of n are ; Ans: ±1, ±3, ±5, ±15

if period of function cos(nx).sin(5x/n) is 3 pi, then number of integral values of n are ;
 
Ans: ±1, ±3, ±5, ±15

Grade:12th pass

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Hello student,
Please find answer to your question
f(x) = cos(nx).sin(\frac{5x}{n})
Period: 3pi
cos(n(x+3\pi )).sin(\frac{5(x+3\pi )}{n}) = cos(nx).sin(\frac{5x}{n})
cos(n(x+\pi )+2n\pi ).sin(\frac{5(x+3\pi )}{n}) = cos(nx).sin(\frac{5x}{n})
cos(x+2\pi ) = cos(x)
cos(n(x+\pi )).sin(\frac{5(x+3\pi )}{n}) = cos(nx).sin(\frac{5x}{n})
cos(nx+n\pi )).sin(\frac{5(x+3\pi )}{n}) = cos(nx).sin(\frac{5x}{n})
cos(x+n\pi ) = cos(x)
-cos(nx)).sin(\frac{5(x+3\pi )}{n}) = cos(nx).sin(\frac{5x}{n})
Solving this equation, we have
n= \pm 1, \pm 3,\pm 5,\pm 15

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