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