t-Formulae

Question 1

t-formulae

Answer 1

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

Question 2

t-formulae derivation

Answer 2

Make a right angled triangle with angle x/2, A 1 and O t then use double angle (cos^2 - sin^2 for cos)