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Chapter 5: Problem 34
Verify each identity. $$\csc ^{2} x \sec x=\sec x+\csc x \cot x$$
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Exercises \(116-118\) will help you prepare for the material covered in the next section. In each exercise, use exact values of trigonometric functions to show that the statement is true. Notice that each statement expresses the product of sines and/or cosines as a sum or a difference. $$\sin \pi \cos \frac{\pi}{2}=\frac{1}{2}\left[\sin \left(\pi+\frac{\pi}{2}\right)+\sin \left(\pi-\frac{\pi}{2}\right)\right]$$
Graph each side of the equation in the same viewing rectangle. If the graphs appear to coincide, verify that the equation is an identity. If the graphs do not appear to coincide, this indicates the equation is not an identity. In these exercises, find a value of \(x\) for which both sides are defined but not equal. $$\frac{\sin x}{1-\cos ^{2} x}=\csc x$$
Will help you prepare for the material covered in the next section.$$\text { Give exact values for } \sin 30^{\circ}, \cos 30^{\circ}, \sin 60^{\circ}, \text { and } \cos 60^{\circ}$$
Will help you prepare for the material covered in the next section. $$\text { Solve: } u^{3}-3 u=0$$
Suppose you are solving equations in the interval \([0,2 \pi)\) Without actually solving equations, what is the difference between the number of solutions of \(\sin x=\frac{1}{2}\) and \(\sin 2 x=\frac{1}{2} ?\) How do you account for this difference?
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