Show that

$$\frac{\cot \theta -\tan \theta }{\cot \theta +\tan \theta }\equiv \cos 2\theta$$

for $\theta \ne \frac{n\pi }{2}$ where $n\in \mathbb{Z}$.

The power output $P$ (in Watts) of a specific AC circuit component is modelled by the function $P(t)=11{\cos }^2(2t-40^{\circ })$, where $t$ is a phase angle measured in degrees and $0^{\circ }\le t<90^{\circ }$.

Determine the values of $t$ for which the power output is exactly $3$ Watts, giving your answers to one decimal place. (Solutions based entirely on graphical or numerical methods are not acceptable.)