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Sin(A+B)Sin(A-B)

If α, β, Y ar...

Question

If $α, β, γ$ are in A.P, then $\frac{{sin}^{2} α - {sin}^{2} γ}{sin α cos α - sin γ cos γ}$ is equal to

A

tan 2 β

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B

cot 2 β

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C

tan (α - γ)

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D

tan β

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Solution

The correct option is A $tan 2 β$
$\frac{{sin}^{2} α - {sin}^{2} γ}{sin α cos α - sin γ cos γ}$
$= \frac{2 sin (α + γ) sin (α - γ)}{sin 2 α - sin 2 γ}$
$= \frac{2 sin (α + γ) sin (α - γ)}{2 sin (α - γ) cos (α + γ)}$
$= tan (α + γ) = tan 2 β$

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Sin(A+B)Sin(A-B)

Standard XI Mathematics

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