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prove the following trigonometric identity

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2 Answers

(2sin2x - 1)/(sinxcosx) = tanx-cotx
(sin2x+sin2x-1)/(sinxcosx)=tanx-cotx
(sin2x-cos2x)/(sinxcosx)=sinx/cosx-cosx/sinx
=sin2x/sinxcosx-cos2x/sinxcosx=(sin2x-cos2x)/(sinxcosx)
 
sorry about mis-step in second line. all is well.
 
  ( 2 Sin2 X - 1 )/ Sin x cosX = tanX - CotX
 
  2 Sin2 X -1      =      sin X  - CosX
  Sin X CosX              cosX     SinX
                               
                                Sin2 X         -     Cos2X   
                                CosXSinX        CosX SinX
                             
                                Sin2X -Cos2 X =
                                   SinX Cos X
                               
                                 Sin2X- 1 + Sin2
                                   Sin X CosX
 
                            =    2 Sin2X - 1
                                Sin X Cos X