Question

rewrite 6tan3x in terms of tan x

Answer 1

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Answer 2

http://answers.yahoo.com/question/index?qid=20110210111657AAK2PMr

Answer 3

@Nicole15 did you get your result.

Answer 4

no @praxer

Answer 5

tan(a+b) = [tan(a) + tan(b)]/[1 - tan (a) * tan (b)]

tan(2x+x) = [tan2x + tanx]/[1 - tan2x * tanx] ........ (1)

tan2x = tan(x+x) = [tanx + tanx]/[1 - tanx * tanx] = 2tanx/(1-(tanx)^2) ........ (2)

Making (2) in (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)/(...

\[tan(3x) = [3tanx - (tanx)^3]/[1-3(tanx)^2]\]

now you have the tan3x formula. So for 6tan3x just multiply a 6 with the result.

Understood it @Nicole15 :)