Sum and Difference Identities

Which of the following is the same as $$\cos\ \left(A+B\right)$$ ?

Which of the following is equivalent to $$\tan\ \left(A-B\right)$$ ? Options: $$\tan\ A\ -\ \tan\ B$$ , $$\frac{\tan\ A\ -\tan\ B}{1+\ \tan A\tan B}$$ , $$\frac{\tan\ A\ +\tan\ B}{1-\ \tan A\tan B}$$ , $$\frac{\sin\ A}{\cos\ B}$$

Expand $$\sin\ \left(33^{o\ }+42^o\right)$$

Expand $$\cos\ \left(\frac{\pi}{5}+\frac{\pi}{6}\right)$$

$$\cos75^o\cos15^o-\sin75^{o\ }\sin15^o$$ is equivalent to

$$\frac{\tan45^o+\tan30^o}{1-\tan45^o\tan30^o}$$ is equivalent to

Use sum or difference angles identity to find the exact value for $$\cos105^o$$

Use sum or difference angles identity to find the exact value for $$\sin\ \left(-15^o\right)$$

Evaluate $$\sin(x+y)$$ given $$\sin x=\frac{3}{5}$$ and $$\sin y=\frac{2}{3}$$ , where $$x$$ and $$y$$ are both in the first quadrant.

cos(175)cos(55)+sin(175)sin(55)