Sum and Difference Formulas
Examples:
1. Find the exact value of \(\sin 15^\circ \). SOLUTION
2. Find the exact value of \( \dfrac{\tan\dfrac{2\pi}{9}-\tan\dfrac{\pi}{18}}{1+\tan\dfrac{2\pi}{9}\tan\dfrac{\pi}{18}}\). 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
4. If \( \cos \alpha = \frac{5}{13},
\frac{3\pi}{2}< \alpha < 2\pi \). Find the exact value of \( \tan
(2\alpha)\). SOLUTION
5. If \(\sin \theta = -\frac{\sqrt 3}{3},
\frac{3\pi}{2}< \theta < 2\pi \). Find the exact value of \( \cos
\frac{\theta}{2}\). SOLUTION
6. Let \( \tan\alpha=-\dfrac{4}{3}, \, \dfrac{\pi}{2} < \alpha < \pi \) and \(\cos\beta=\dfrac{1}{3}, \, 0 < \beta < \dfrac{\pi}{2} \). Find the exact value of (a) \( \sin (\alpha - \beta) \) (b) \( \cos\dfrac{\alpha}{2} \) (c) \(\tan(2\beta) \) SOLUTION