91Ó°ÊÓ

Find the exact value of each expression using double-angle identities. $$ \tan \left(60^{\circ}\right) $$

Find the products. \((\sin \alpha+2)(\sin \alpha-2)\)

Find the exact value of each expression using double-angle identities. $$ \sin (2 \pi / 3) $$

Factor each trigonometric expression. \(\tan ^{2} \alpha-6 \tan \alpha+8\)

Use identities to simplify each expression. Do not use a calculator. \(\sin ^{2}\left(\frac{\pi}{5}\right)-\cos ^{2}\left(\frac{\pi}{5}\right)\)

Verify that each equation is an identity. $$ \frac{\cos (\alpha+\beta)}{\cos \alpha+\sin \beta}=\frac{\cos \alpha-\sin \beta}{\cos (\beta-\alpha)} $$

Simplify each expression. \(\tan (-\beta) \csc (-\beta) \cos (\beta)\)

Match each expression with an equivalent expression from \((a)-(h)\) Do not use a calculator: a. \(\cos (0)\) b. \(-\cos \left(44^{\circ}\right)\) c. \(-\tan \left(44^{\circ}\right)\) d. \(\cot \left(\frac{5 \pi}{14}\right)\) e. \(-\cos \left(46^{\circ}\right)\) f. \(\csc \left(\frac{\pi-2}{2}\right)\) g. \(\sin \left(46^{\circ}\right)\) h. \(\sin \left(44^{\circ}\right)\) $$ \tan \left(\frac{\pi}{7}\right) $$

Simplify each expression by applying the odd/even identities, cofunction identities, and cosine of a sum or difference identities. Do not use a calculator: $$ \cos \left(4^{\circ}\right) \cos \left(9^{\circ}\right)+\cos \left(86^{\circ}\right) \cos \left(81^{\circ}\right) $$

Simplify each expression by applying the odd/even identities, cofunction identities, and cosine of a sum or difference identities. Do not use a calculator $$ \sin (\pi / 2-z) \cos (-z)-\cos (\pi / 2-z) \sin (-z) $$