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

2 Answers

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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


=> `((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)`

w1nnuha's profile pic

w1nnuha | Student, College Freshman | eNotes Newbie

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