amandalundgreen amandalundgreen

21-12-2016
Mathematics

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Verify the identity. Show your work.
cos(α - β) - cos(α + β) = 2 sin α sin β

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Peytiii2829 Peytiii2829

23-12-2016

cos (a-b) = cos(a)cos(b) + sin(a)sin(b)
cos (a+b) = cos(a)cos(b) - sin(a)sin(b)
so, cos(a-b) - cos(a+b) =

=cos(a)cos(b) + sin(a)sin(b) - [cos(a)cos(b) - sin(a)sin(b)]
=2sin(a)sin(b)

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