Question
Sun April 18, 2010 By:

Prove the following

Expert Reply
Mon April 19, 2010

(tan22x - tan2x)/(1 - tan22x tan2x) =

Using a2 - b2 = (a+b)(a-b), for numerator and denominator,

[(tan2x - tanx)(tan2x + tanx)]/[(1 - tan2x tanx) (1 + tan2x tanx)] =

= tan3x tanx

Using,

tan (x+y) = (tanx + tany)/(1 - tanxtany)

(tan2x - tanx)/(1 + tan2x tanx) = tan (2x - x) = tanx

and (tan2x + tanx)/(1 - tan2x tanx) = tan (2x+x) = tan3x.

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