Math

How can I prove this identity?

(1 + sinØ + cosØ):(1 - sinØ + cosØ) =
(1 + sinØ) : cosØ

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asked by Lucia
  1. Work on the left hand side:
    (1 + sinØ + cosØ)/(1 - sinØ + cosØ)
    multiply both the numerator and denominator by (1-sinφ+cosφ) and simplify:
    ((1+cosφ)^2-sin&hi;^2)/(1-sinφ+cosφ)^2
    =2cosφ(1+cosφ)/[2(1-sinφ)(1+cosφ)]
    =2cosφ/[2(1-sinφ)]
    =cosφ/(1-sinφ)
    Now multiply top and bottom by (1+sinφ)
    cosφ(1+sinφ)/(1-sin²φ)
    =cosφ(1+sinφ)/cos²φ
    =(1+sinφ)/cosφ

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