Trigonometry - Multiple angle formulas

1. $sin3\alpha=3sin\alpha-4sin^3\alpha=3cos^2\alpha.sin\alpha-sin^3\alpha$

2. $sin4\alpha=4sin\alpha.cos\alpha-8sin^3\alpha.cos\alpha$

3. $sin5\alpha=5sin\alpha-20sin^3\alpha+16sin^5\alpha$

4. $cos3\alpha=4cos^3\alpha-3cos\alpha=cos^3\alpha-3cos\alpha.sin^2\alpha$

5. $cos4\alpha=8cos^4\alpha-8cos^2\alpha+1$

6. $cos5\alpha=16cos^5\alpha-20cos^3\alpha+5cos\alpha$

7. $tan3\alpha={3tan\alpha-tan^3\alpha \over 1-3tan^2\alpha }$

8. $tan4\alpha={{4tan\alpha-4tan^3\alpha } \over 1-6tan^2\alpha+tan^4\alpha}$

9. $tan5\alpha={{tan^5\alpha-10tan^3\alpha+5tan\alpha } \over 1-10tan^2\alpha+5tan^4\alpha}$

10. $cot 3 \alpha={cot^3\alpha-3cot\alpha \over3cot^2\alpha-1}$

11. $cot4\alpha={1-6tan^2\alpha+tan^4\alpha \over 4tan\alpha-4tan^3\alpha}$

12. $cot5\alpha={1-10\,tan^2\, \alpha+5\,tan^4\, \alpha \over tan^5 \, \alpha-10\,tan^3\, \alpha+5tan\, \alpha}$