### Trigonometry

goals
Trignometry is helpful in triangle based mathematical analysis. One of various trigonometric relation is tan (A+B) $= \frac{tan A + tan B}{1- tan A tan B}$.
Now consider a diagram representing a triangular roof frame ABC with a window frame EFC. BC and EF are horizontal and AD and FC are vertical.
If $\dfrac {\sin^{3}\theta+\cos^{3}\theta}{\sin \theta+\cos \theta}+\dfrac {\sin^{3}\theta-\cos^{3}\theta}{\sin \theta-\cos \theta}=K$,  then K =
If $7 (\theta) = (2n + 1)\pi$, when $n = 0, 1, 2, 3, 4, 5, 6,$ then
On the basis of above information, answer the following questions:
If $\tan A=\sqrt{3}$, then verify that $\sin^{2}A+\cos^{2}A=1$.
State if the given angles are conterminal.
$\alpha =185^{\circ}, \beta =-545^{\circ}$