if `f(x)=(sin (x+alpha)/(sin(x+beta))),alpha ne beta ` then f(x) has

Options

A. maximum at x=0
B. minimum at x=0
C. neither maximum nor minimum
D. non of these

Answer

C

Explanation

We have `f(x)=(sin(x+alpha))/(sin(x+beta)`
Clearly f(x) is defined for all ` x ne - beta`
Now `f(x)=(sin(x + beta)cos(a+alpha)-cos(x+beta)sin(x+ alpha))/(sin^2 (x + beta))`
`rArr f(x)=(sin(beta -alpha))/(sin^2(x+beta))ne 0 as alpha ne beta`
Hence f(x) has neither a maximum nor a minimum .