### Trigonometry

goals
$\frac{{\sin \,\theta \, - \,2\,{{\sin }^3}\,\theta }}{{2\,{{\cos }^3}\theta \, - \,\cos \,\theta }}\, = \,\tan \,\theta$
The value of $\sin ( 360^o - \theta)$ is
From the following figure,
From the top of a building, $60$ metres high, the angles of depression of the top and bottom of a vertical lamp-post are observed to be ${30}^{o}$ and ${60}^{o}$ respectively. Find:
The value of $\sin { \left( {{ 45 }}^{o} +\theta \right) } -\cos { \left( {{ 45 }}^{o} -\theta \right) }$ is