Verify that (tanx-sinx)/(tanx+sinx)=(secx-1)/(secx+1)

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The identity `(tanx-sinx)/(tanx+sinx)=(secx-1)/(secx+1)` has to be verified

`(tanx-sinx)/(tanx+sinx)`

=> `((sin x/cos x)-sinx)/((sin x/cos x)+sinx)`

=> `(sin x(1/cos x-1))/(sin x(1/cos x+1))`

=> `(1/cos x-1)/(1/cos x+1)`

=> `(sec x - 1)/(sec x + 1)`

This proves that `(tanx-sinx)/(tanx+sinx)=(secx-1)/(secx+1)`

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w1nnuha | Student, College Freshman | eNotes Newbie

Posted on

(tanx-sinx)/(tanx+sinx)=(sinx/cosx-sinx)/(sinx/cosx+sinx)

                                  =sinx(1/cosx-1)/sinx(1/cosx+1)

(since secx=1/cosx)     =(secx-1)/(secx+1)

                                                                              CQFD

 

 

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