What is the fundamental period of `f(x) = (sin x+ sin 3x)/(cos x+ cos 3x)`

Options

A. `pi//2`
B. `pi`
C. `2pi`
D. `3pi`

Answer

B

Explanation

`f(x)=(sinx+sin3x)/(cosx+cos3x)`
`=(2sin2xcosx)/(2cos2x cos3x)`
where `x ne (2n+1)(pi)/(4),(2n+1)(pi)/(2)`
`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.