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lim(alpha to beta)[(sin^(2)alpha-sin^(2)...

`lim_(alpha to beta)[(sin^(2)alpha-sin^(2)beta)/(alpha^(2)-beta^(2))]` is equal to

A

0

B

1

C

`(sinbeta)/(beta)`

D

`(sin2beta)/(2beta)`

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(alphatobeta)(lim)(sin^(2)alpha-sin^(2)beta)/(2alpha-0)`
`=underset(alphatobeta)(lim)(sin2alpha)/(2alpha)=(sin2beta)/(2beta)`
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Knowledge Check

  • Suppose alpha, beta in R , and let E=sin^(2)(alpha+beta)+sin^(2)alpha+sin^(2)beta-2cos alpha cos beta cos (alpha+beta) then E is equal to :

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