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Question Number 189375 by moh777 last updated on 15/Mar/23
      show that :      (1/(cscx + cot x)) = cscx − cot x
showthat:1cscx+cotx=cscxcotx
Answered by Ar Brandon last updated on 15/Mar/23
(1/(cscx+cotx))=((sinx)/(1+cosx))=((sinx(1−cosx))/(1−cos^2 x))  =((sinx(1−cosx))/(sin^2 x))=((1−cosx)/(sinx))  =cscx−cotx
1cscx+cotx=sinx1+cosx=sinx(1cosx)1cos2x=sinx(1cosx)sin2x=1cosxsinx=cscxcotx
Answered by BaliramKumar last updated on 15/Mar/23
LHS = (1/(cosecx + cotx)) = ((cosec^2 x − cot^2 x)/(cosecx + cotx))               = (((cosecx + cotx)(cosecx − cotx))/((cosecx + cotx)))                = cosecx − cotx = RHS
LHS=1cosecx+cotx=cosec2xcot2xcosecx+cotx=(cosecx+cotx)(cosecxcotx)(cosecx+cotx)=cosecxcotx=RHS
Answered by manxsol last updated on 15/Mar/23
recall     cosec^2 =1+cot^2 x   (1/(cscx + cot x)) ×((cscx−cotx)/(cscx−cotx))=  ((cscx−cotx)/(csc^2 x−ct^2 x))=cscx−cotx
recallcosec2=1+cot2x1cscx+cotx×cscxcotxcscxcotx=cscxcotxcsc2xct2x=cscxcotx

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