12. Trigonometric Identities

Simplify the expression.

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

Simplify the expression.

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

Simplify the expression.

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

Use the Pythagorean identities to rewrite the expression with no fraction.

$\(\frac{1}{1-\sec\theta}\)$

Select the expression with the same value as the given expression.

$\(\sec\[\left\)(-\(\frac{4\pi}{5}\]\right\))$

Identify the most helpful first step in verifying the identity.

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

Use the even-odd identities to evaluate the expression.

$\(\cos\]\left\)(-\(\theta\[\right\))-\(\cos\]\theta\)$

Select the expression with the same value as the given expression.

$\(\sin\[\left\)(-38\(\degree\]\right\))$

Use the Pythagorean identities to rewrite the expression as a single term.

$\(\left\)(1+\(\csc\[\theta\]\right\))\(\left\)(1-\(\csc\[\theta\]\right\))$

Use the even-odd identities to evaluate the expression.

$-\(\cot\]\left\)(\(\theta\[\right\))\(\cdot\]\sin\[\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\))$