# Trig triangle problem

1. Apr 14, 2009

### crazy_v

1. The problem statement, all variables and given/known data

Use the given triangle to prove that for 0 < X <90, 1 + tan^2X = 1 / cos^2X

(the given triangle is right angled with angle X marked. The hypotenuse is labeled c, adjacent angle is labeled a and the opposite angle is labeled b)

3. The attempt at a solution

I have no idea where to begin,
tanX = b/a
cosX = a/c

2. Apr 14, 2009

### tiny-tim

Welcome to PF!

Hi crazy_v! Welcome to PF!
But you're there

just put b/a and a/c into the original equation, and you have … ?

3. Apr 14, 2009

### Cyosis

Since $$\cos \theta=\frac{a}{c} \Rightarrow \cos^2 \theta=\frac{a^2}{c^2}$$. Write c^2 in terms of a and b now, hint Pythagoras.

4. Apr 14, 2009

### crazy_v

thanks guys

yeah that looks a lot more obvious now, thanks anyways