1. ## Trigonometry

Don’t know where to start here

The length of a diagonal of a rectangle is 10cm. The diagonal is inclined at an angle $\theta^{\circ}$ to a side of the rectangle. Show that the perimeter, P cm, of the rectangle is given by:

$P = 20\sqrt{2}\sin(\theta + 45)^{\circ}$

2. $AC=10, \ \widehat{CAD}=\theta$

$CD=10\sin\theta, \ AD=10\cos\theta$

$P=20(\sin\theta+\cos\theta)=20\left(\sin\theta+\si n\left(\frac{\pi}{2}-\theta\right)\right)=20\cdot2\sin\frac{\pi}{4}\cos \left(\frac{\pi}{4}-\theta\right)=$

$=20\sqrt{2}\sin\left(\frac{\pi}{4}+\theta\right)$