Question #de713

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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#