6. Analytic Trigonometry

Simplify the expression.

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

Identify the most helpful first step in verifying the identity.

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

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.

$\sec (-\frac{4\pi }{5})$

Simplify the expression.

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

Identify the most helpful first step in verifying the identity.

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

Use the even-odd identities to evaluate the expression.

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

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

$\sin (-38°)$

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

$(1+\csc \theta )(1-\csc \theta )$

Simplify the expression.

${\tan }^2\theta -{\sec }^2\theta +1$

Use the even-odd identities to evaluate the expression.

$\cos (-\theta )-\cos \theta$