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Trigonometry - Transforming of trigonometric expressions to product

  1. \(sin\alpha+sin \beta=2sin{{\alpha+\beta} \over 2}. cos{{\alpha-\beta} \over 2}\)
  2. \(sin\alpha-sin \beta=2cos{{\alpha+\beta} \over 2}. sin{{\alpha-\beta} \over 2}\)
  3. \(cos\alpha+cos\beta=2cos{\alpha+\beta \over 2 }.cos{\alpha-\beta \over 2 }\)
  4. \(cos\alpha-cos\beta=-2sin{\alpha+\beta \over 2 }.sin{\alpha-\beta \over 2 }\)
  5. \(tan\,\alpha+tan\,\beta={sin(\alpha+\beta) \over cos \,\alpha.cos \,\beta}\)
  6. \(tan\,\alpha-tan\,\beta={sin(\alpha-\beta) \over cos \,\alpha.cos \,\beta}\)
  7. \(cot\,\alpha+cot\,\beta={sin(\beta+\alpha) \over sin \,\alpha.sin \,\beta}\)
  8. \(cot\,\alpha-cot\,\beta={sin(\beta-\alpha) \over sin \,\alpha.sin \,\beta}\)
  9. \(cos\,\alpha+sin \, \alpha=\sqrt{2}cos\bigg({\pi \over4}-a\bigg)=\sqrt{2}sin\bigg({\pi \over4}+a\bigg)\)
  10. \(cos\,\alpha-sin \, \alpha=\sqrt{2}sin\bigg({\pi \over4}-a\bigg)=\sqrt{2}cos\bigg({\pi \over4}+a\bigg)\)
  11. \(tan \,\alpha+cot \,\beta={cos(\alpha-\beta) \over cos\,\alpha.sin\,\beta}\)
  12. \(tan \,\alpha-cot \,\beta=-{cos(\alpha+\beta) \over cos\,\alpha.sin\,\beta}\)
  13. \(1+cos\,\alpha=2cos^2{\alpha \over 2}\)
  14. \(1-cos\,\alpha=2sin^2{\alpha \over 2}\)
  15. \(1+sin\,\alpha=2cos^2 \Big({\pi \over 4}-{\alpha \over 2} \Big)\)
  16. \(1-sin\,\alpha=2sin^2 \Big({\pi \over 4}-{\alpha \over 2} \Big)\)