Sum and Difference Formulas

Lecture video on Sum and Difference Formulas

Examples:

1. Find the exact value of  \(\sin 15^\circ \).   SOLUTION

2. Find the exact value of  \( \frac{\tan\frac{2\pi}{9}-\tan\frac{\pi}{18}}{1+\tan\frac{2\pi}{9}\tan\frac{\pi}{18}}\).    SOLUTION

3. Find the exact value of \( \cos \frac{5\pi}{12}\, \cos \frac{\pi}{12} + \sin \frac{5\pi}{12}\, \sin \frac{\pi}{12} \).    SOLUTION

Establish each Identity.

1. \(\displaystyle{\frac{\cos (\alpha - \beta)}{\cos \alpha \cos \beta } = 1 + \tan \alpha \tan \beta}\)   SOLUTION

2. \(\displaystyle{\frac{\cos (\alpha + \beta)}{\cos \alpha \cos \beta } = 1 - \tan \alpha \tan \beta}\)   SOLUTION

3. \(\displaystyle{\frac{\sin (\alpha - \beta)}{\cos \alpha \cos \beta } = \tan \alpha - \tan \beta}\)   SOLUTION

4. \(\displaystyle{\frac{\cos (\alpha - \beta)}{\sin \alpha \sin \beta } = \cot \alpha \cot \beta + 1}\)   SOLUTION

5. \(\displaystyle{\tan\left( \theta + \frac{\pi}{2}\right) = -\cot\theta}\)   SOLUTION

6. Simplify the expression.  \(\cos\left(\tan^{-1}\frac{4}{3}+\cos^{-1}\frac{12}{13}\right)\)