i need help solving this problem

(seca-tana)^2=1-sina/1+sina

any help would be appreciated

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- Nov 10th 2008, 05:17 PMspeedy229trig proofs
i need help solving this problem

(seca-tana)^2=1-sina/1+sina

any help would be appreciated - Nov 10th 2008, 06:12 PMrugbygirl2
First thing with trig proofs, you need to decide which side to work with, its best to limit your self to solving one side.

I would start with factoring out (seca-tana)^2 - Nov 10th 2008, 06:21 PMSoroban
Hello, speedy229!

Quote:

$\displaystyle (\sec\theta-\tan\theta)^2\:=\:\frac{1-\sin\theta}{1+\sin\theta}$

Multiply the right side by $\displaystyle \frac{1-\sin\theta}{1-\sin\theta}\!:$

. . $\displaystyle \frac{1-\sin\theta}{1+\sin\theta}\cdot{\color{blue}\frac{1-\sin\theta}{1-\sin\theta}} \;\;=\;\;\frac{(1-\sin\theta)^2}{1-\sin^2\!\theta} \;\;=\;\;\frac{(1-\sin\theta)^2}{\cos^2\!\theta}$

. . $\displaystyle = \;\;\left(\frac{1-\sin\theta}{\cos\theta}\right)^2 \;\;=\;\;\left(\frac{1}{\cos\theta} - \frac{\sin\theta}{\cos\theta}\right)^2 \;\;=\;\;(\sec\theta - \tan\theta)^2$

- Nov 11th 2008, 04:34 AMspeedy229trig proofs
thanks for the help but i need to solve for 1-sina/1+sina

i have problem solved to this point (1-sina)(1+sina/1-sin^2a this is where i'm stuck!!!!

(Worried)(Worried) - Nov 11th 2008, 04:39 AMmr fantastic
- Nov 11th 2008, 07:48 AMrugbygirl2
I think what you mean is that the answer in the back of your book has

(1-sina)/(1+sina)= (1-sina)/(1+sina) as the proof for the identities.

If that is the case start with the left side of the equation (seca-tana)^2 and use your identities to work towards the (1-sina)/(1+sina).

Soroban just proved the identity by working on the right side first, I'm sure your instructor will tell you that either method is a valid solution.