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How to prove this identity

tan3x - tan2x- tanx = tan3xtan2xtanx

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Michael F. | Mathematics TutorMathematics Tutor
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tan3x - tan2x- tanx=tan(2x+x)-tan2x-tanx=(tan2x+tanx)/(1-tan2xtanx)-(tan2x+tanx)
=(tan2x+tanx)(1/(1-tan2xtanx)-1)=(tan2x+tanx)(1-(1-tan2xtanx))/(1-tan2xtanx)
=(tan2x+tanx)(tan2xtanx/(1-tan2xtanx)=[(tan2x+tanx)/(1-tan2xtanx)]tan2xtanx=tan3xtan2xtanx