5)+Extra+Identities

Introduction
This is a list of the extra identities, or in other words, those identities which are either rarely seen or rarely used. You won't be using these equations most of the time, but still, if you have mastered the basics of Trigonometry, feel free to explore these equations! This is supplementary so take your time :D.



Product-sum Identities
sin s + sin t = 2 sin (s+t)/2 cos (s-t)/2

sin s - sin t = 2 cos (s+t)/2 sin (s-t)/2

cos s + cos t = 2 cos (s+t)/2 cos (s-t)/2

cos s - cos t = -2 sin (s+t)/2 sin (s-t)/2

Product Identities
 sin s * cos t = (sin (s+t) + sin (s-t))/2

 cos s * cos t = (cos (s+t) + cos (s-t))/2

 sin s * sin t = (cos (s-t) - cos (s+t))/2

Triple Angle Formulas
 sin 3//t// = 3 sin //t// – 4 sin3 //t//

 cos 3//t// = 4 cos3 //t// –3 cos //t//

//tan 3 //t = (3 tan t - tan^3 t)/(1-3 tan^2 t)

 *Note: These formulas can be easily obtained from the addition and double angle formulas.

Advancing Half-Angle Formulas
 sin t = (2 tan t/2)/(1 + tan^2 t/2)

 cos t = (1 - tan^2 t/2)/(1 + tan^2 t/2)

 tan t = (2 tan t/2)/(1 - tan^2 t/2)

Conclusion
 It wasn't that hard was it! You just need to memorise these identities to come up with the solutions :D.