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Let f(x) = {{:(-2 sin x,"for",-pi le x l...

Let `f(x) = {{:(-2 sin x,"for",-pi le x le - (pi)/(2)),(a sin x + b,"for",-(pi)/(2) lt x lt (pi)/(2)),(cos x,"for",(pi)/(2) le x le pi):}`. If f is continuous on `[-pi, pi)`, then find the values of a and b.

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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