91Ó°ÊÓ

Find the exact value of each expression. $$ \tan \left[\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right] $$

(a) \(\sin (\alpha+\beta)\) (b) \(\cos (\alpha+\beta)\) (c) \(\sin (\alpha-\beta)\) (d) \(\tan (\alpha-\beta)\) $$ \sin \alpha=\frac{3}{5}, 0<\alpha<\frac{\pi}{2} ; \quad \cos \beta=\frac{2 \sqrt{5}}{5},-\frac{\pi}{2}<\beta<0 $$

Use a calculator to find the approximate value of each expression rounded to two decimal places. \(\cos ^{-1}(-0.44)\)

Establish each identity. $$\tan ^{2} \theta \cos ^{2} \theta+\cot ^{2} \theta \sin ^{2} \theta=1$$

Find the exact value of each of the following under the given conditions: (a) \(\sin (\alpha+\beta)\) (b) \(\cos (\alpha+\beta)\) (c) \(\sin (\alpha-\beta)\) (d) \(\tan (\alpha-\beta)\) $$ \cos \alpha=\frac{\sqrt{5}}{5}, 0<\alpha<\frac{\pi}{2} ; \quad \sin \beta=-\frac{4}{5},-\frac{\pi}{2}<\beta<0 $$

Establish each identity. $$ \frac{\cos (4 \theta)-\cos (8 \theta)}{\cos (4 \theta)+\cos (8 \theta)}=\tan (2 \theta) \tan (6 \theta) $$

Find the exact value of each expression. $$ \tan \left[\sin ^{-1}\left(-\frac{1}{2}\right)\right] $$

Give a general formula for all the solutions List six solutions. \(\sin \theta=\frac{1}{2}\)

Use a calculator to find the approximate value of each expression rounded to two decimal places. \(\cos ^{-1} \frac{\sqrt{2}}{3}\)

Establish each identity. $$\sec ^{4} \theta-\sec ^{2} \theta=\tan ^{4} \theta+\tan ^{2} \theta$$