Question
tan3x=(3tanx-tan^3x)/(1-3tan^2x)
Answers
Reiny
LS = tan(3x)
= tan(2x + x)
= (tan2x + tanx)/(1- tan2x tanx)
= [2tanx/(1-tan^2 x) + tanx ] / [(1 - 2tanx(tanx)/(1 - tan^2 x) ]
multiply top and bottom by 1 - tan^2 x
(2tanx + tanx + tan^3 x)/(1 - tan^2 x - tan^2 x)
= (3tanx + tan^3 x)/(1 - 3tan^2 x)
= RS
= tan(2x + x)
= (tan2x + tanx)/(1- tan2x tanx)
= [2tanx/(1-tan^2 x) + tanx ] / [(1 - 2tanx(tanx)/(1 - tan^2 x) ]
multiply top and bottom by 1 - tan^2 x
(2tanx + tanx + tan^3 x)/(1 - tan^2 x - tan^2 x)
= (3tanx + tan^3 x)/(1 - 3tan^2 x)
= RS