Ask Me Help Desk - Proving trigonometric identities

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proving trigonometric identities

how do you prove

(cosx/ (1+sinx) ) + ((1+sinx)/cosx) = 2secx

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

$=\frac{cos^{2}(x)+1+2sin(x)+sin^{2}(x)}{cos(x)(1+s in(x))}$

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

Now, factor the numerator, cancel and see what remains.

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