Prove the following identities.
$\(\sec\]\theta\)=\(\frac{1}{\cos\theta}\)$

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\))$

Identify the most helpful first step in verifying the identity.

$\(\sec\)^3\(\theta\)=\(\sec\]\theta\)+\(\frac{\tan^2\theta}{\cos\theta}\)$

Find all solutions to the equation.

$\(\left\)(\(\cos\[\theta\)+\(\sin\]\theta\[\right\))\(\left\)(\(\cos\]\theta\)-\(\sin\[\theta\]\right\))=-\(\frac\)12$

Find all solutions to the equation where 0 ≤ $\(\theta\)$ ≤ $2\(\pi\)$.

$\(\sin\]\theta\[\cos\]\left\)(2\(\theta\[\right\))-\(\sin\]\left\)(2\(\theta\[\right\))\(\cos\]\theta\)=\(\frac{\sqrt2}{2}\)$

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

What are the three Pythagorean identities for the trigonometric functions?