Question

Complete the identity. sin (α+β) sin (α-β) = ?

Answer 1

google trig identities or look in the book
it is there

Answer 2

satellite would you do the sum identity then the difference identity and lastly the product identity to solve it?

Answer 3

\(
\sin(A+B) = \sin(A)\cos(B) + \cos(A)\sin(B) \\
\sin(A-B) = \sin(A)\cos(B) - \cos(A)\sin(B) \\
\sin(A+B)\sin(A-B) = \{ \sin(A)\cos(B) + \cos(A)\sin(B) \}* \\
\{ \sin(A)\cos(B) - \cos(A)\sin(B) \} =
\sin^2(A)\cos^2(B) - \cos^2(A)\sin^2(B) = \\
(1-\cos^2(A))\cos^2(B) - \cos^2(A)(1-cos^2(B)) = \\
\cos^2(B) - \cos^2(A)\cos^2(B) - \cos^2(A) + \cos^2(A)\cos^2(B) = \\
\cos^2(B) - \cos^2(A)
\)

Answer 4

\( \Large
\sin(\alpha+\beta)\sin(\alpha-\beta) = \cos^2(\beta) - \cos^2(\alpha)
\)

Answer 5

Thank you so much!