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Question Number 10695 by okhema last updated on 23/Feb/17
prove that tanx−cotx=−2cot2x
provethattanx−cotx=−2cot2x
Answered by nume1114 last updated on 23/Feb/17
tan x−cot x =((sin x)/(cos x))−((cos x)/(sin x)) =((sin^2 x−cos^2 x)/(sin xcos x)) =((−(cos^2 x−sin^2 x))/((1/2)×2sin xcos x)) =−2((cos 2x)/(sin 2x)) =−2cot 2x
tanx−cotx=sinxcosx−cosxsinx=sin2x−cos2xsinxcosx=−(cos2x−sin2x)12×2sinxcosx=−2cos2xsin2x=−2cot2x
Commented by okhema last updated on 23/Feb/17
i dnt understand how you come about with the fourth line come down
idntunderstandhowyoucomeaboutwiththefourthlinecomedown
Commented by nume1114 last updated on 23/Feb/17
i used double angle fomulas: sin 2x=2sin xcos x cos 2x=cos^2 x−sin^2 x
iuseddoubleanglefomulas:sin2x=2sinxcosxcos2x=cos2x−sin2x
Answered by bar Jesús last updated on 24/Feb/17
((senx)/(cosx))−((cosx)/(senx))= −2cot2x ((sen^2 x−cos^2 x)/(senxcosx))= −2cot2x senxcosx=((sen2x)/2) −(cos^2 x−sen^2 x)= sen^2 x−cos^2 x= −cos2x ((−cos2x)/((sen2x)/2))= −2cot2x ((−2cos2x)/(sen2x))= −2cot2x −cot2x= −2cot2x
senxcosx−cosxsenx=−2cot2xsen2x−cos2xsenxcosx=−2cot2xsenxcosx=sen2x2−(cos2x−sen2x)=sen2x−cos2x=−cos2x−cos2xsen2x2=−2cot2x−2cos2xsen2x=−2cot2x−cot2x=−2cot2x
Commented by bar Jesús last updated on 24/Feb/17
jojojojo, excuse me −2cot2x= −2cot2x
jojojojo,excuseme−2cot2x=−2cot2x

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