# Math Help - Trig Proof

1. ## Trig Proof

So last night I was doing a trig proof and found the solution easily enough but someone else tried to do it a different way and I for the life of me couldn't find any way to do it besides going around in circles to prove.I think it's quite challenging but you might not.

Solve for the left(Work on the right)

tanB+1 = secB+cscB(secB+cscB)
tanB-1 = secB-cscB(secB+cscB)

2. That identity doesn't look right to me. For instance, the left hand side is not defined for B = pi/4, because the denominator becomes zero. On the other, the right hand side _is_ defined for B=pi/4.

3. Hello, fvvfz!

I agree with Happy Joe . . . There is a typo.

I believe you are missing parentheses on the right.

$\text{Prove: }\;\frac{\tan\theta + 1}{\tan\theta - 1} \:=\:\frac{(\sec\theta + \csc \theta)(\sec\theta + \csc\theta)}{(\sec\theta - \csc\theta)(\sec\theta + \csc\theta)}$

$\text{Cancel and we have: }\;\frac{\sec\theta + \csc\theta}{\sec\theta - \csc\theta} \;=\;\dfrac{\dfrac{1}{\cos\theta} + \dfrac{1}{\sin\theta}}{\dfrac{1}{\cos\theta} - \dfrac{1}{\sin\theta}}$

$\text{Multiply by }\frac{\sin\theta\cos\theta}{\sin\theta\cos\theta}\!:\;\;\frac{\sin\theta\cos\theta\left(\dfrac{1}{\cos\theta} + \dfrac{1}{\sin\theta}\right)} {\sin\theta\cos\theta \left(\dfrac{1}{\cos\theta} - \dfrac{1}{\sin\theta}\right)} \;=\;\frac{\sin\theta + \cos\theta}{\sin\theta - \cos\theta}$

$\text{Divide numerator and denominator by }\cos\theta\!:$

. . . . . . $\frac{\dfrac{\sin\theta}{\cos\theta} + \dfrac{\cos\theta}{\cos\theta}}{\dfrac{\sin\theta}{\cos\theta} - \dfrac{\cos\theta}{\cos\theta}} \;=\;\frac{\tan\theta + 1}{\tan\theta - 1}$