Cos/1+sin + cos/1-sin =2 sec

kathlyniciousz · Jan 30, 2011, 03:20 AM

Please help me to answer this. Thank you! :) LOVE.love!

galactus · Jan 30, 2011, 05:01 AM

$\frac{cos(x)}{1+sin(x)}+\frac{cos(x)}{1-sin(x)}=2sec(x)$

Like when adding any fraction, get the denominators the same.

$\frac{(1-sin(x))cos(x)}{(1-sin(x))(1+sin(x))}+\frac{cos(x)(1+sin(x))}{(1-sin(x))(1+sin(x))}$

$\frac{(1-sin(x))cos(x)+cos(x)(1+sin(x))}{(1-sin(x))(1+sin(x))}$

Notice the denominator is the factored form of the difference of two squares, and the numerator simplifies to 2cos(x):

$\frac{2cos(x)}{1-sin^{2}(x)}$

$\frac{2cos(x)}{cos^{2}(x)}$

$\frac{2}{cos(x)}$

$2sec(x)$

kathlyniciousz · Jan 30, 2011, 01:10 PM

Thank you so much GALACTUS!

kathlyniciousz · Jan 30, 2011, 01:12 PM

Anyway, I was wrong. I should put it how to prove that. :/ thank you so much for responding!

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