# Proving Trig Identities.

• May 3rd 2009, 03:04 PM
zweevu
Proving Trig Identities.
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?
• May 3rd 2009, 07:57 PM
mr fantastic
Quote:

Originally Posted by zweevu
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 $\cos \alpha = \frac{1}{5}$, $\cos \beta = \frac{5}{7}$ and $\cos \gamma = \frac{19}{35}$.

Now evaluate $\cos (\alpha + \beta + \gamma)$ by applying the compound angle formula several times.

Note: Find $\sin \alpha$, $\sin \beta$ and $\sin \gamma$ by using the known values for cos and applying the Pythagorean Identity.