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show that tan3x-tan2x-tanx =tan3x*tan2x*tanx

Consider 3x = 2x + x

⇒ tan( 3x) = tan(2x + x)

⇒ tan( 3x) =

⇒ tan( 3x) (1 - tan(2x) tan(x)) = tan(2x) + tan(x)

⇒ tan(3x) - tan(3x) tan(2x) tan(x) =  tan(2x) + tan(x)

⇒ tan(3x) - tan(2x) - tan(x) = tan(x) tan(2x) tan(3x)

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hi!  heres the answer to ur quest...

here we are using the formula . tah(a-b) = tana-tanb/1-tana tanb.

taking first two terms, tan(3x - 2x) = tan3x - tan2x / 1 - tan3x tan2x

implies, tanx = tan3x - tan 2x / 1- tan3x tan2x

 implies , tanx - tanx tan3x tan2x = tan3x - tan2x

 hence, on rearranging, tan3x - tan2x - tanx = tan3x tan2x tanx .

hence proved.  All the best!

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ana the formula tan(a-b) = tana-tanb/1+tana tanb

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 3x=2x+x
applying tan
tan3x = tan(2x+x)
tan3x = tan2x+tanx1-tan2xtanx
tan3x(1-tan2xtanx) = tan2x+tanx
tan3x-tan3xtan2xtanx = tan2x+tanx
tan3x-tan2x-tanx = tan3xtan2xtanx
L.H.S=R.H.S

  • 19

dude it s very simple just write tan3x as tan 2x +x and expand it and arrange it
it is in ncert or rd sharma class 12

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