Proving trigonometric identites using basic identities

• Jun 20th 2010, 10:43 PM
mastermin346
Proving trigonometric identites using basic identities
prove the following identities

a) $\frac{1}{1+sin\theta}+\frac{1}{1-sin\theta}=2sec^2\theta$
• Jun 20th 2010, 10:49 PM
Hello mastermin346
Quote:

Originally Posted by mastermin346
prove the following identities

a) $\frac{1}{1+sin\theta}+\frac{1}{1-sin\theta}=2sec^2\theta$

$\dfrac{1}{1+\sin\theta}+\dfrac{1}{1-\sin\theta}=\dfrac{(1-\sin\theta)+(1+\sin\theta)}{(1-\sin\theta)(1+\sin\theta)}$
$=\dfrac{2}{1-\sin^2\theta}$

$=\dfrac{2}{\cos^2\theta}$

$=2\sec^2\theta$
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