Question #de713

Question

1031 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-14T01:30:42

$LHS=tan3x$

$=tan(x+2x)$

$=(tanx+tan2x)/(1-tanxtan2x)$

$=(tanx+(2tanx)/(1-tan^2x))/(1-(tanx*2tanx)/(1-tan^2x)$

$=((tanx(1-tan^2x)+2tanx)/(1-tan^2x))/((1-tan^2x-2tan^2x)/(1-tan^2x))$

$= (3tanx-tan^3(x))/(1-3tan^2(x))=RHS$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$LHS=sin4x$

$=2sin2xcos2x$

$=4sinxcosx(1-2sin^2x)$

$=cosx*4sinx(1-2sin^2x)$

$=(cosx)(4sinx-8sin^3x)=RHS$