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  • What is the fundamental period of f(x)=sinx+sin3x/cosx+cos3x ?

What is the fundamental period of f(x)=sinx+sin3x/cosx+cos3x ?

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Solution:

f(x)=sinx+sin3x/cosx+cos3x\ \=2sin2x cosx/2cos2x cosx=tan2x

Where \ x eq (2n+1)pi /4,(2n+1)pi /2\ \ Rightarrow f(x+pi /2)=tan2(x+pi /2)=tan(2x+pi )=tan2x

It seems that pi /2  is a period but it is not because f(0) is defined

where as f(pi /2) is not defined

Thus , period is pi.

Posted by

Deependra Verma

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