Question

what is sec^2 theta-tan^2theta=1 prove it

Answer 1

well lets switch this into sin and cos

\[\frac{ 1 }{ \cos^2\theta } - \frac{ \sin^2\theta }{\cos^2\theta } = 1\]

which becomes

\[\frac{ 1 - \sin^2\theta }{ \cos^2\theta } = 1\]

Now knowing that there is a trig property where

\[\sin^2\theta = \cos^2\theta = 1\]

Solve that for cos^2theta

\[1-\sin^2\theta = \cos^2\theta\]

So this means in the original that the 1-sin^2theta = cos^2theta so you can replace it with that

\[\frac{ \cos^2\theta }{ \cos^2\theta } = 1\]
\[1=1\]

This is your proof

Answer 2

should be sin^2theta + cos^2theta = 1 in middle there