# Prove Id

• May 12th 2011, 07:08 PM
reallylongnickname
Prove Id
sec^2 = 1 + tan^2

or

csc^2 = 1 + cot^2
• May 12th 2011, 07:15 PM
TheEmptySet
Quote:

Originally Posted by reallylongnickname
sec^2 = 1 + tan^2

or

csc^2 = 1 + cot^2

Just divide the Pythagorean identity by cosine

$\sin^2(x)+\cos^2(x)=1 \iff \frac{\sin^2(x)}{\cos^2(x)}+\frac{\cos^2(x)}{\cos^ 2(x)}=\frac{1}{\cos^2(x)}$

Now just simplify

See if you can get other one
• May 12th 2011, 07:33 PM
reallylongnickname
$csc^2(x) = 1 + cot^2(x)\longleftrightarrow \frac{1}{ sin^2(x)}-\frac{cos^2(x)}{sin^2(x)} = 1$