Addition formulae | Mathematico

We would like to know how to calculate something like

\sin (A + B) and \cos (A + B)

or, indeed, $\tan (A + B) .$

The correct formulas are fairly simple:

\sin (A \pm B) = \sin A \cos B \pm \cos A \sin B

and

\cos (A \pm B) = \cos A \cos B \mp \sin A \sin B

The formula for $\tan$ can be worked out from these two, and you'll be asked to do that (with hints!) in one of the problems.

The angles $x$ and $y$ are such that $\sin (x) = \frac{2}{5}$ and $\cos (y) = \frac{1}{4} .$

Given that $x$ is obtuse and $y$ is acute, find the exact value of

\cos (x + y) and \sin (y - x)