Question

Prove that tan 3x= 3tanx - tan^3x/1-3tan^3x

Answer 1

Hi ,

1 ) tan2x

= tan( x + x )

= ( tanx + tanx )/( 1 - tanxtanx)

= 2tanx/( 1 - tan² x ) ---( a )

Now ,

tan3x

= tan( 2x + x )

= ( tan2x + tanx )/( 1 - tan2xtanx )

= [ 2tanx/( 1 - tan² x ) + tanx ]/{[1-(2tanx/(1 -tan² x)]tanx }

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

= ( 2tanx + tanx-tan³x) /( 1 - 3tan²x )

= ( 3tanx - tan³ x ) / ( 1 - 3tan²x )

Hence proved.

I hope this helps you.

: )