8 812 New Member Joined Feb 25, 2011 Messages 28 Location The gates of Mt Olympus Gender Female HSC 2012 Jan 21, 2012 #1 Prove: sin(5x) + sin(3x) - 2sin(2x)cos(x) = 2sin(2x)cos(3x)
nightweaver066 Well-Known Member Joined Jul 7, 2010 Messages 1,585 Gender Male HSC 2012 Jan 21, 2012 #2 812 said: Prove: sin(5x) + sin(3x) - 2sin(2x)cos(x) = 2sin(2x)cos(3x) Click to expand... LHS: sin(5x) + sin(3x) - 2sin(2x)cos(x) = 2sin(4x)cos(x) - 2sin(2x)cos(x) = 2cos(x)[sin(4x) - sin(2x)] =2cos(x)[2cos(3x)sin(x)] = 2sin(2x)cos(3x) = RHS
812 said: Prove: sin(5x) + sin(3x) - 2sin(2x)cos(x) = 2sin(2x)cos(3x) Click to expand... LHS: sin(5x) + sin(3x) - 2sin(2x)cos(x) = 2sin(4x)cos(x) - 2sin(2x)cos(x) = 2cos(x)[sin(4x) - sin(2x)] =2cos(x)[2cos(3x)sin(x)] = 2sin(2x)cos(3x) = RHS
