# trig proofs

• Nov 10th 2008, 05:17 PM
speedy229
trig proofs
i need help solving this problem
(seca-tana)^2=1-sina/1+sina
any help would be appreciated
• Nov 10th 2008, 06:12 PM
rugbygirl2
First thing with trig proofs, you need to decide which side to work with, its best to limit your self to solving one side.
• Nov 10th 2008, 06:21 PM
Soroban
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 AM
speedy229
trig 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 AM
mr fantastic
Quote:

Originally Posted by speedy229
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)

Your post makes no sense. Soroban has solved the problem for you!

By the way, just in case you think it's an equation that has to be solved for a ..... It's NOT. It's an identity (as Soroban has clearly shown) and is true for all values of a.
• Nov 11th 2008, 07:48 AM
rugbygirl2
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.