show that :   tan3x.tan2x.tanx = tan3x-tan2x-tanx

Asked by aniket.vyas002 | 6th Jul, 2016, 04:53: PM

Expert Answer:

begin mathsize 14px style Consider comma
3 straight x minus 2 straight x equals straight x space
Applying space tan space on space both space sides comma space
tan left parenthesis 3 straight x minus 2 straight x right parenthesis space equals tan space straight x space
rightwards double arrow fraction numerator left parenthesis tan space 3 straight x minus space tan space 2 straight x right parenthesis over denominator left parenthesis 1 plus tan space 2 straight x space tan space 3 straight x right parenthesis end fraction equals tan space straight x
rightwards double arrow tan space 3 straight x minus tan space 2 straight x space equals tanx space plus space tanx space tan space 2 straight x space tan space 3 straight x space
rightwards double arrow tan space 3 straight x minus tan space 2 straight x space minus tan space straight x equals tan space straight x space tan space 2 straight x space tan space 3 straight x
rightwards double arrow tan space 3 straight x space tan space 2 straight x space tan space straight x space equals space tan space 3 straight x space minus space tan space 2 straight x space minus space tan space straight x space space space space space..... left parenthesis proved right parenthesis end style

Answered by Rashmi Khot | 7th Jul, 2016, 09:34: AM