prove the following trigonometric identity

Question

2sin^2x - 1÷ sinxcosx = tanx-cotx

Answer 1

 

  ( 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 + Sin²X 

                                   Sin X CosX

 

                            =    2 Sin²X - 1

                                Sin X Cos X

Answer 2

(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.