91Ó°ÊÓ

For the angle \(x\) (in radians) that satisfies the given conditions, use double-angle identities to find the exact values of \(\sin 2 x, \cos 2 x,\) and \(\tan 2 x.\) $$\csc x=-\frac{5}{3} \text { and } \frac{3 \pi}{2}< x<2 \pi$$

In Exercises \(9-14\), show that the given equations are not identities. $$\cos 2 x=2 \cos x$$

For the angle \(x\) (in radians) that satisfies the given conditions, use double-angle identities to find the exact values of \(\sin 2 x, \cos 2 x,\) and \(\tan 2 x.\) $$\sec x=-\frac{6}{5} \text { and } \pi< x<\frac{3 \pi}{2}$$

In Exercises \(7-20,\) find the exact value of each of the given expressions. $$\sin \left(-45^{\circ}\right) \cos \left(30^{\circ}\right)$$

In Exercises \(15-20,\) write each expression in terms of \(\sin x\) and/or \(\cos x\) only. $$\cot x \csc x$$

Find the exact solutions of the given equations, in radians. $$\sin ^{2} x=1$$

In Exercises \(15-20,\) write each expression in terms of \(\sin x\) and/or \(\cos x\) only. $$\csc ^{2} x$$

For the angle \(x\) (in radians) that satisfies the given conditions, use double-angle identities to find the exact values of \(\sin 2 x, \cos 2 x,\) and \(\tan 2 x.\) $$\csc x=\frac{9}{7} \text { and } 0< x<\frac{\pi}{2}$$

In Exercises \(7-20,\) find the exact value of each of the given expressions. $$\cos \left(-30^{\circ}\right) \sin \left(45^{\circ}\right)$$

Find the exact solutions of the given equations, in radians. $$\cos ^{2} x=1$$