Posted by Yadira on Monday, May 14, 2012 at 7:15pm.
I think the parentheses are in the wrong place. It should probably read:
(1-cos2x)/tan x = sin2x
Again, split everything into sin and cos, and don't forget the identities:
cos(2x)=cos²(x)-sin²(x)
sin(2x)=2sin(x)cos(x)
(1-cos(2x))/tan(x)
=(1-(cos²(x)-sin²(x))*(cos(x)/sin(x))
=(1-(1-2sin²(x))*cos(x)/sin(x)
=2sin²(x)*cos(x)/sin(x)
=2sin(x)cos(x)
=sin(2x)
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