The function `(sin(x+a))/(sin(x+b))` has no maxima or minima if `b-a=npi,n in I` `b-a=(2n+1)pi,n in I` `b-a=2npi,n in I` (d) none of these

Options

A. `b-a=npi,n in I`
B. `b-a=(2n+1)pi, n in I`
C. `b-a =2n pi, n in I`
D. none of these

Answer

1,2,3

Explanation

`f(x)=(sin(x+a))/(sin(x+b))`
`f(x) =(sin(x+b)cos(x+a)-sin(x+a)cos(x+b))/(sin^(2)(x+b))`
`=(sin(b-a))/(sin^(2)(x+b))`
if sin(b-a)=0 then f(x) =0 or f(x) will be a constant
i.e `b-a=npi or b-a =(2n+1)pior b-a=2npi`
Then f(x) has no minima