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July 26, 2014

Posted by **Lucia** on Tuesday, May 31, 2011 at 1:14pm.

(1 + sinØ + cosØ):(1 - sinØ + cosØ) =

(1 + sinØ) : cosØ

- Math -
**MathMate**, Tuesday, May 31, 2011 at 5:23pmWork 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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