# Simplifying the trigonometric equation

$$\sin(x)\cos(x)\tan(x) + \frac{2\sin(x)\cos^3(x)}{\sin(2x)}$$

Can someone please show me step by step working of how I may be able to solve this?

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a) What's the definition of $\tan x$, b) double-angle formula for $\sin (2x)$. –  Daniel Fischer Aug 22 '13 at 9:41
That's an expression, not an equation. I assume you mean "simplify," in which case you'll want to recall the definition of tangent and some double-angle identities. –  T. Bongers Aug 22 '13 at 9:42
Sorry. I'm looking to simplify using the trigonometrical identities. –  Sugi Aug 22 '13 at 9:46

Hint:

1. $$2\sin(x)\cos(x)=\sin(2x)$$ 2. $$\sin(x)\cos(x)\tan(x)=\sin^2(x)$$ 3. $$\sin^2(x)+\cos^2(x)=1$$

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Hi. How does sin(x)cos(x)tan(x)= sin^2(x)? –  Sugi Aug 22 '13 at 10:02
@Sugi If$$\sin(x)\cos(x)\tan(x)=\sin(x)\cos(x)\frac{\sin(x)}{\cos(x)}=\frac{\sin^2(x) \cos(x)}{\cos(x)}=\sin^2(x)$$ –  Alizter Aug 22 '13 at 10:10
Thank you. Makes sense. –  Sugi Aug 22 '13 at 10:16