SOLUTION: Prove identity: 2sin(-x)-cotx*sinx*cosx=(sinx-1)^2-2

SOLUTION: Prove identity: 2sin(-x)-cotxsinxcosx=(sinx-1)^2-2

Question 1057233: Prove identity:
2sin(-x)-cotx*sinx*cosx=(sinx-1)^2-2
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
2sin(-x)-cotx*sinx*cosx=(sinx-1)^2-2
-2sin (x)-[(cos x/sin x)*sin x* cos x)], because sin is an odd function.
-2 sin x-cos^2 x=
-2sin x-1+sin^2 x, since cos ^2 x=1-sin^2 x
=sin^2x-2sin x -1
=(sin x-1)^2-2, since the first term is sin^2x-2sin x+1, and we need to get to -1.

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