Trigonometric Identities

$$\begin{eqnarray*} \mr {\sin(-\theta)}{-\sin(\theta)}% {\cos(-\theta)}{\cos(\theta)} \mr {\sin(A+B)}{\sin(A)\cos(B)+\cos(A)\sin(B)}% {\cos(A+B)}{\cos(A)\cos(B)-\sin(A)\sin(B)} \mr {\sin^2(\theta)}{\frac{1-\cos(2\theta)}{2}}% {\cos^2(\theta)}{\frac{1+\cos(2\theta)}{2}} \mr {\sin(A)\sin(B)}{\frac{\cos(A-B) - \cos(A+B)}{2}}% {\cos(A)\cos(B)}{\frac{\cos(A+B) + \cos(A-B)}{2}} \mr {\sin(A)\cos(B)}{\frac{\sin(A+B) + \sin(A-B)}{2}}% {\cos(A)\sin(B)}{\frac{\sin(A+B) - \sin(A-B)}{2}} \mr {\sin(A)+\sin(B)}{2\sin\left(\frac{A+B}{2}\right)\cos\left(\frac{A-B}{2}\right)}% {\cos(A)+\cos(B)}{-2\cos\left(\frac{A+B}{2}\right)\cos\left(\frac{A-B}{2}\right)} \end{eqnarray*}$$