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If f(x) is continuous over [-pi, pi], wh...

If f(x) is continuous over `[-pi, pi]`, where f(x) is defined as
`f(x) = {(-2sin x, ",",-pi le x le (-pi)/2),(alpha sin x + beta, ",", -(pi)/2 lt x lt (pi)/2 ),(cos x, ",", (pi)/2 le x lt pi ):}`
then `alpha` and `beta` equals

A

`alpha=1, beta=1`

B

`alpha=-1, beta=-1`

C

`alpha=-1, beta=1`

D

`alpha=1, beta=-1`

Text Solution

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The correct Answer is:
C
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