Question

tan3x =3tanx-tan³x÷1-3tan²x prove that

Answer 1

Hi ,

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we know that ,

tan( A + B ) = ( tanA + tanB )/( 1 - tanAtanB )


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Now ,

tan 2x = tan( x + x )

= [ tanx + tanx ] / [ 1 - tanx tanx ]

= ( 2tan x )/ ( 1 - tan² x ) ----( 1 )

tan 3x = tan( x + 2x )

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

= [tanx+(2tanx/(1-tan²x)]/[1-tanx(2tanx/1-tan²x)]

=[tanx(1-tan²x)+2tanx]/[1-tan²x-tanx×2tanx]

=( tanx -tan³x + 2tanx )/( 1 - tan²x - 2tan²x )

= ( 3tanx - tan³ x ) / ( 1 - 3tan²x )

Hence proved.

I hope this helps you.

: )