rewrite tan3x in terms of tanSolutiontan3x in terms of tanx

rewrite tan3x in terms of tan

Solution

tan(3x) in terms of tanx

Trig Indentity : tan(a +b) = (tana +tanb)/(1 - tana*tanb)

So, tan3x = tan(2x+x)

= (tan2x +tanx)/( 1- tan2x*tanx) -----(1)

We know tan2x = 2tanx/( 1-tan^2x). Substituting tan2x in equation (1)

tan(3x) = [2tanx/(1-(tanx)^2) + tanx]/ [1 - 2tanx/(1-(tanx)^2) * tanx]
tan(3x) = [(2tanx + tanx - (tanx)^3)/((1-(tanx)^2))]/[1 - (2(tanx)^2)/(1-(tanx)^2)]
tan(3x) = [(3tanx - (tanx)^3)/(1-(tanx)^2)]/[(1-(tanx)^2 - 2(tanx)^2)/(1-(tanx)^2)]
tan(3x) = [(3tanx - (tanx)^3)/(1-(tanx)^2)]/[(1-3(tanx)^2)/(...
tan(3x) = [3tanx - (tanx)^3]/[1-3(tanx)^2]