lim α → β sin 2 α − sin 2 β α 2 − β 2 is equal to Options: A . &nbsp sin 3 β ( 4 β ) B . &nbsp sin 2 β ( 2 β ) C . &nbsp sin 8 β ( 7 β ) D . &nbsp sin 6 β ( 4 β )

Answer: Option B : B lim α → β sin 2 α − sin 2 β α 2 − β 2 = lim α → β sin ( α − β ) sin ( α + β ) ( α − β ) ( α + β ) = sin 2 β ( 2 β )

limα→βsin2α−sin2βα2−β

Question -

$lim α \to β \frac{{sin}^{2} α - {sin}^{2} β}{α^{2} - β^{2}}$ is equal to

Options:

A .

\frac{sin 3 β}{(4 β)}

B .

\frac{sin 2 β}{(2 β)}

C .

\frac{sin 8 β}{(7 β)}

D .

\frac{sin 6 β}{(4 β)}

Answer: Option B
:
B

lim α \to β \frac{{sin}^{2} α - {sin}^{2} β}{α^{2} - β^{2}} = lim α \to β \frac{sin (α - β) sin (α + β)}{(α - β) (α + β)} = \frac{sin 2 β}{(2 β)}

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