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

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

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\))$

Use the even-odd identities to evaluate the expression.

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

Use the even-odd identities to evaluate the expression.

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

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

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