Trigonometry - Transforming of trigonometric expressions to sum

  1. \(sin\,\alpha.sin\,\beta={cos(\alpha-\beta)-cos(\alpha+\beta) \over 2}\)
     
  2. \(cos\,\alpha.cos\,\beta={cos(\alpha-\beta)+cos(\alpha+\beta) \over 2}\)
     
  3. \(sin\,\alpha.cos\,\beta={sin(\alpha-\beta)+sin(\alpha+\beta) \over 2}\)
     
  4. \(tan \,\alpha.tan\, \beta={tan \,\alpha+tan \,\beta \over cot\, \alpha+ cot\, \beta }\)
     
  5. \(cot \,\alpha.cot\, \beta={cot\, \alpha+ cot\, \beta \over tan \,\alpha+tan \,\beta }\)
     
  6. \(tan \,\alpha.cot\, \beta={tan\, \alpha+ cot\, \beta \over cot \,\alpha+tan \,\beta }\)