Proving 1 + tan^2X = 1 / cos^2X for 0 < X < 90 in a Right Triangle

[crazy_v]

Homework Statement

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)

The Attempt at a Solution

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

 

[tiny-tim]

Welcome to PF!

Hi crazy_v! Welcome to PF!

Use the given triangle to prove that for 0 < X <90, 1 + tan^2X = 1 / cos^2X
…
tanX = b/a
cosX = a/c

But you're there …

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

 

[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.

 

[crazy_v]

thanks guys

yeah that looks a lot more obvious now, thanks anyways