91Ó°ÊÓ

In \(3-17,\) find the exact value of \(\tan (A+B)\) and of \(\tan (A-B)\) for each given pair of values. $$ A=\frac{5 \pi}{6}, B=\frac{5 \pi}{6} $$

In \(3-17,\) find the exact value of \(\tan (A+B)\) and of \(\tan (A-B)\) for each given pair of values. $$ A=\frac{\pi}{3}, B=\frac{\pi}{4} $$

If \(\sin A=-\frac{24}{25}\) and \(540^{\circ} < A < 630^{\circ},\) find: a. \(\sin \frac{1}{2} A\) b. \(\cos \frac{1}{2} A\) c. \(\tan \frac{1}{2} A\)

In \(3-26,\) prove that each equation is an identity. $$ \frac{1}{\sin \theta \cos \theta}-\frac{\sin \theta}{\cos \theta}=\cot \theta $$

\(\ln 3-17,\) find the exact value of \(\sin (A-B)\) and of \(\sin (A+B)\) for each given pair of values. \(A=\frac{\pi}{3}, B=\frac{5 \pi}{4}\)

In \(9-20,\) for each given function value, find \(a \cdot \sin 2 \theta, \mathbf{b} \cdot \cos 2 \theta, \mathbf{c} \cdot \tan 2 \theta, \mathbf{d}\) . the quadrant in which 2\(\theta\) lies. Show all work. \(\csc \theta=\sqrt{5}\) in the second quadrant

In \(3-17,\) find the exact value of \(\cos (A+B)\) for each given pair of values. \(A=\frac{\pi}{4}, B=\frac{\pi}{6}\)

a. Find the exact value of \(\cos 15^{\circ}\) by using \(\cos \left(45^{\circ}-30^{\circ}\right)\) b. Use the value of \(\cos 15^{\circ}\) found in a to find \(\cos 165^{\circ}\) by using \(\cos \left(180^{\circ}-15^{\circ}\right)\) c. Use the value of \(\cos 15^{\circ}\) found in a to find \(\cos 345^{\circ}\) by using \(\cos \left(360^{\circ}-15^{\circ}\right)\) d. Use \(\cos A=\sin \left(90^{\circ}-A\right)\) to find the exact value of \(\sin 75^{\circ} .\)

In \(3-26,\) prove that each equation is an identity. $$ \frac{\sin ^{2} \theta}{1+\cos \theta}=1-\cos \theta $$

a. Find the exact value of \(\cos 75^{\circ}\) by using \(\cos \left(45^{\circ}+30^{\circ}\right)\) b. Use the value of \(\cos 75^{\circ}\) found in a to find \(\cos 255^{\circ}\) by using \(\cos \left(180^{\circ}+75^{\circ}\right)\) c. Use \(\cos A=\sin \left(90^{\circ}-A\right)\) to find the exact value of \(\sin 15^{\circ} .\)