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Chapter 5: Problem 15
Verify the identity. $$\cos ^{2} \beta-\sin ^{2} \beta=1-2 \sin ^{2} \beta$$
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Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$\sec ^{2} x+0.5 \tan x-1=0$$
Use inverse functions where needed to find all solutions of the equation in the interval \([0,2 \pi)\). $$\tan ^{2} x-\tan x-2=0$$
Use inverse functions where needed to find all solutions of the equation in the interval \([0,2 \pi)\). $$\tan ^{2} x+\tan x-12=0$$
Find the exact value of each expression. (a) \(\sin \left(315^{\circ}-60^{\circ}\right)\) (b) \(\sin 315^{\circ}-\sin 60^{\circ}\)
Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$\frac{1+\sin x}{\cos x}+\frac{\cos x}{1+\sin x}=4$$
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