If `y=(sin(x+a))/(sin(x+b)),a!=b`, then `y` is

Options

A. minima at `x=0`
B. maxima at `x=0`
C. neither minima nor maxima at `x=0`
D. None of the above

Answer

C

Explanation

Given `y=(sin(x+a))/(sin(x+b))`
`implies(dy)/(dx)=(sin(x+b)cos(x+a)-sin(x+a)cos(x+b))/(sin^(2)(x+b))`
`implies(dy)/(dx)=(sin(b-a))/(sin^(2)(x+b))`
For maxima or minima put `(dy)/(dx)=0`
`impliessin(b-a)=0`
It means no value of x it is neither maxima nor minima.