# Trig

• Nov 20th 2008, 11:13 PM
xwrathbringerx
Trig
http://www.mathhelpforum.com/math-he...9-untitled.bmp

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.
• Nov 21st 2008, 11:19 AM
masters
Quote:

Originally Posted by xwrathbringerx
http://www.mathhelpforum.com/math-he...9-untitled.bmp

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..,

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

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

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

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

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

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

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

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