91Ó°ÊÓ

In Exercises \(59-68\), verify each identity. $$\sin ^{2} \frac{\theta}{2}=\frac{\sec \theta-1}{2 \sec \theta}$$

Find the exact value of the following under the given conditions: (A) .\(\cos (\alpha+\beta)\) (B). \(\sin (\alpha+\beta)\) (C) \(\tan (\alpha+\beta)\) \(\tan \alpha=-\frac{3}{4}, \alpha\) lies in quadrant II, and \(\cos \beta=\frac{1}{3}, \beta\) lies in quadrant I.

Verify each identity. $$\frac{\sin x+\cos x}{\sin x}-\frac{\cos x-\sin x}{\cos x}=\sec x \csc x$$

Solve the equation on the interval \([0,2 \pi)\) $$\cos x-2 \sin x \cos x=0$$

Find the exact value of the following under the given conditions: (A) .\(\cos (\alpha+\beta)\) (B). \(\sin (\alpha+\beta)\) (C) \(\tan (\alpha+\beta)\) \(\tan \alpha=-\frac{4}{3}, \alpha\) lies in quadrant II, and \(\cos \beta=\frac{2}{3}, \beta\) lies in quadrant I.

In Exercises \(59-68\), verify each identity. $$\sin ^{2} \frac{\theta}{2}=\frac{\csc \theta-\cot \theta}{2 \csc \theta}$$

Verify each identity. $$\frac{\sin 2 x+(\sin 3 x+\sin x)}{\cos 2 x+(\cos 3 x+\cos x)}=\tan 2 x$$

Find the exact value of the following under the given conditions: (A) .\(\cos (\alpha+\beta)\) (B). \(\sin (\alpha+\beta)\) (C) \(\tan (\alpha+\beta)\). \(\cos \alpha=\frac{8}{17}, \alpha\) lies in quadrant IV, and \(\sin \beta=-\frac{1}{2}, \beta\) lies in quadrant III.

Solve the equation on the interval \([0,2 \pi)\) $$\tan ^{2} x \cos x=\tan ^{2} x$$

Verify each identity. $$4 \cos x \cos 2 x \sin 3 x=\sin 2 x+\sin 4 x+\sin 6 x$$