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The function (sin(x+a))/(sin(x+b)) has n...

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

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

Text Solution

Verified by Experts

The correct Answer is:
1,2,3
`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
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