Prove that cos^-1(1/5)+cos^-1(5/7)+cos^-1(19/35) = Pie without the use of a calculator? How would I do this?
Several approaches are possible. One approach might be the following:
Let $\displaystyle \cos \alpha = \frac{1}{5}$, $\displaystyle \cos \beta = \frac{5}{7}$ and $\displaystyle \cos \gamma = \frac{19}{35}$.
Now evaluate $\displaystyle \cos (\alpha + \beta + \gamma)$ by applying the compound angle formula several times.
Note: Find $\displaystyle \sin \alpha$, $\displaystyle \sin \beta$ and $\displaystyle \sin \gamma$ by using the known values for cos and applying the Pythagorean Identity.