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Chapter 5: Problem 32
Write each expression as the sine, cosine, or tangent of an angle. Then find the exact value of the expression. $$\frac{\tan \frac{\pi}{5}+\tan \frac{4 \pi}{5}}{1-\tan \frac{\pi}{5} \tan \frac{4 \pi}{5}}$$
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Solve each equation on the interval \([0,2 \pi)\) $$10 \cos ^{2} x+3 \sin x-9=0$$
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. $$\cos \frac{\pi}{2} \cos \frac{\pi}{3}=\frac{1}{2}\left[\cos \left(\frac{\pi}{2}-\frac{\pi}{3}\right)+\cos \left(\frac{\pi}{2}+\frac{\pi}{3}\right)\right]$$
Determine whether each statement makes sense or does not make sense, and explain your reasoning. The most efficient way that I can simplify \(\frac{(\sec x+1)(\sec x-1)}{\sin ^{2} x}\) is to immediately rewrite the expression in terms of cosines and sines.
Will help you prepare for the material covered in the first section of the next chapter. Solve each equation by using the cross-products principle to clear fractions from the proportion: If \(\frac{a}{b}=\frac{c}{d},\) then \(a d=b c,(b \neq 0 \text { and } d \neq 0)\) Round to the nearest tenth. $$\text { Solve for } B: \frac{51}{\sin 75^{\circ}}=\frac{71}{\sin B}$$
Use the most appropriate method to solve each equation on the interval \([0,2 \pi) .\) Use exact values where possible or give approximate solutions correct to four decimal places. $$3 \tan ^{2} x-\tan x-2=0$$
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