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harbi · Jun 2, 2007, 08:33 PM

Prove the following identities:

1 + sin theta / 1 - sin theta = sec squared theta + 2 tan theta sec theta + tan squared theta

1 + sec theta / 1- sec theta = 1 - 2 cosec squared theta - 2 cot theta cosec theta

galactus · Jun 3, 2007, 04:11 AM

Prove the following identities:

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

I will get you started, then give me your thoughts.

Multiply the left side by $\frac{1+sin{\theta}}{1+sin{\theta}}$

$\frac{1+sin{\theta}}{1-sin{\theta}}\cdot\frac{1+sin{\theta}}{1+sin{\theta }}$

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

Now, continue? Remember what $1-sin^{2}{\theta}$ is equal to?