0. Functions

Find all solutions to the equation.

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

Identify the most helpful first step in verifying the identity.

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

Simplify the expression.

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

Simplify the expression.

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

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\)=\(\frac{\sqrt2}{2}\)$

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\))$