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If f(x)={m x+1\ \ \ ,\ \ \ xlt=pi/2,\ \ ...

If `f(x)={m x+1\ \ \ ,\ \ \ xlt=pi/2,\ \ \ \ \ \sinx+n\ \ \ ,\ \ \ x >pi/2` is continuous at `x=pi/2` , then `m=1,\ \ n=0` (b) `m=(npi)/2+1` (c) `n=(mpi)/2` (d) `m=n=pi/2`

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Verified by Experts

Correct option is C)
Since, f(x) is continuous at `x=π/2`​
∴`​lim​_(x→π/2−)(mx+1)`
`=​lim​_(x→π/2+)(sinx+n)`
`⇒mπ/2​+1=sinπ/2​+n`
...
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