Trig

**xwrathbringerx** · November 20th 2008, 11:13 PM

Diagonals = 2 units

(a) Find AD and DC in terms of θ.

(b) Show that DX = sin2θ.

(c) Hence deduce that sin2θ = 2sinθcosθ

Could someone please show me how to start this question? I've been pondering on it for ages.

**masters** · November 21st 2008, 11:19 AM

Originally Posted by xwrathbringerx

Diagonals = 2 units

(a) Find AD and DC in terms of θ.

(b) Show that DX = sin2θ.

(c) Hence deduce that sin2θ = 2sinθcosθ

Could someone please show me how to start this question? I've been pondering on it for ages.

Hello xwrath..,

$\sin \theta=\frac{DC}{2}$

$\boxed{DC=2\sin \theta}$

$\cos \theta=\frac{AD}{2}$

$\boxed{AD=2\cos \theta}$

$\sin \theta=\frac{DX}{2\cos \theta}$

$\boxed{DX=2\sin \theta \cos \theta}$

$\boxed{\sin 2\theta=2\sin \theta \cos \theta}$

$\boxed{DX=\sin 2\theta}$

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