How do i show: \sin^2(x+y)-\sin^2(x-y)\equiv\sin(2x)\sin(2y)

Ingrid Senior 2022-03-01 Answered
How do i show:
sin2(x+y)sin2(xy)sin(2x)sin(2y)
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Expert Answer

Malaika Ridley
Answered 2022-03-02 Author has 6 answers
(sin(x+y))2(sin(xy))2=(sinxcosy+cosxsiny)2(sinxcosy+cosxsiny)2
=(sin2cos2y+2sinxcosycosxsiny+cos2xsin2y)(sin2cos2y2sinxcosycosxsiny+cos2xsin2y)
=4sinxcosycosxsiny
=(2sinxcosx)(2sinycosy)
=sin(2x)sin(2y)
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meizhen85ulg
Answered 2022-03-03 Author has 6 answers
Known Identity
sin2a=1cos2a2
cosxcosy=2sin(xy2)sin(x+y2)
Given
sin2(x+y)sin2(xy)
=1cos2(x+y)(1cos2(xy))2
=cos2(xy)cos2(x+y)2
=sin(2x)sin(2y)
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