1. The alternating voltage,$V$, in an electrical circuit, $t$ seconds after it is switched on, is modelled by the function

$V=20$cos $\pi t+20\sqrt{3}$sin $\pi t$

where $t$ is measured in seconds.

Use the identity $R$cos$( \pi t- \alpha )=R$cos $\alpha$cos $\pi t+R$sin $\alpha$sin $\pi t$ to show that

$20$cos $\pi t+20\sqrt{3}$sin $\pi t$

can be written as

$40cos( \pi t-\frac{ \pi }{3}).$