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

\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)

Thank you so much GALACTUS!

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