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The value of alpha, which satisfy int(pi...

The value of `alpha`, which satisfy `int_(pi/2) ^(alpha) sin x dx = sin2alpha (alpha in [0,2pi]` are equal

A

`(pi)/(2)`

B

`(3pi)/(2)`

C

`(7pi)/(6)`

D

all of these

Text Solution

Verified by Experts

The correct Answer is:
D
`int_(pi//2)^(alpha)sinxdx=sin2alpha,alphain(0,2pi)`
`implies-[cosx]_(pi//2)^(alpha)=sin2alpha`
`implies-cosalpha=sin2alpha`
`implies sin(alpha-(pi)/(2))=sin2alpha`
Hence, `alpha=(pi)/(2),(3pi)/(2),(7pi)/(6)`
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