0. Functions

Simplify the expression.

$\(\tan\)^2\(\theta\)-\(\sec\)^2\(\theta\)+1$

Simplify the expression.

$\(\frac{\tan\left(-\theta\right)}{\sec\left(-\theta\right)}\)$

Simplify the expression.

$\(\left\)(\(\frac{\tan^2\theta}{\sin^2\theta}\)-1\(\right\))\(\csc\)^2\(\left\)(\(\theta\[\right\))\(\cos\)^2\(\left\)(-\(\theta\]\right\))$

Identify the most helpful first step in verifying the identity.

$\(\left\)(\(\frac{\tan^2\theta}{\sin^2\theta}\)-1\(\right\))=\(\sec\)^2\(\theta\[\sin\)^2\(\left\)(-\(\theta\]\right\))$

Prove the following identities.

$\(\sec\]\theta\)=\(\frac{1}{\cos\theta}\)$

Prove the following identities.

$\(\tan\]\theta\)=\(\frac{\sin\theta}{\cos\theta}\)$

Prove the following identities.

$\(\frac{\sin\theta}{1+\cos\theta}\)=\(\frac{1-\cos\theta}{\sin\theta}\)$

Prove the following identities.

$\(\tan\)2\(\theta\)=\(\frac{2\tan\theta}{1-\tan^2\theta}\)$