91Ó°ÊÓ

\(\ln 3-17,\) find the exact value of \(\sin (A-B)\) and of \(\sin (A+B)\) for each given pair of values. \(A=270^{\circ}, B=30^{\circ}\)

In \(3-26,\) prove that each equation is an identity. $$ \csc \theta(\sin \theta+\tan \theta)=1+\sec \theta $$

In \(3-8,\) for each value of \(\theta,\) use double-angle formulas to find a. \(\sin 2 \theta,\) b. \(\cos 2 \theta,\) c. \(\tan 2 \theta .\) Show all work. $$ \theta=\frac{7 \pi}{6} $$

In \(3-8,\) for each value of \(\theta,\) use half-angle formulas to find a. \(\sin \frac{1}{2} \theta\) b. \(\cos \frac{1}{2} \theta\) c. \(\tan \frac{1}{2} \theta .\) Show all work. $$ \theta=\frac{7 \pi}{2} $$

In \(3-17,\) find the exact value of \(\cos (A+B)\) for each given pair of values. \(A=180^{\circ}, B=45^{\circ}\)

In \(3-17,\) find the exact value of \(\tan (A+B)\) and of \(\tan (A-B)\) for each given pair of values. $$ A=180^{\circ}, B=60^{\circ} $$

\(\ln 3-17,\) find the exact value of \(\sin (A-B)\) and of \(\sin (A+B)\) for each given pair of values. \(A=60^{\circ}, B=90^{\circ}\)

In \(3-14,\) write each expression as a single term using \(\sin \theta, \cos \theta,\) or both. $$ \tan ^{2} \theta+1 $$

In \(3-8,\) for each value of \(\theta,\) use double-angle formulas to find a. \(\sin 2 \theta,\) b. \(\cos 2 \theta,\) c. \(\tan 2 \theta .\) Show all work. $$ \theta=\frac{5 \pi}{3} $$

In \(3-17,\) find the exact value of \(\cos (A-B)\) for each given pair of values. \(A=60^{\circ}, B=90^{\circ}\)