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Magazine Problem 20
In Exercises \(15-22,\) write each expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression. $$1-2 \sin ^{2} \frac{\pi}{12}$$
Problem 21
Find the exact value of each expression. $$\tan \left(\frac{\pi}{6}+\frac{\pi}{4}\right)$$
Problem 21
In Exercises \(15-22,\) write each expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression. $$\frac{2 \tan \frac{\pi}{12}}{1-\tan ^{2} \frac{\pi}{12}}$$
Problem 21
Find all solutions of each equation. $$4 \sin \theta-1=2 \sin \theta$$
Problem 21
Be sure that you've familiarized yourself with the second set of formulas presented in this section by working \(5-8\) in the Concept and Vocabulary Check. Express each sum or difference as a product. If possible, find this product's exact value. $$\sin \frac{\pi}{12}-\sin \frac{5 \pi}{12}$$
Problem 21
Verify each identity. $$\frac{\tan ^{2} t}{\sec t}=\sec t-\cos t$$
Problem 22
Find all solutions of each equation. $$5 \sin \theta+1=3 \sin \theta$$
Problem 22
In Exercises \(15-22,\) write each expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression. $$\frac{2 \tan \frac{\pi}{8}}{1-\tan ^{2} \frac{\pi}{8}}$$
Problem 22
Be sure that you've familiarized yourself with the second set of formulas presented in this section by working \(5-8\) in the Concept and Vocabulary Check. Express each sum or difference as a product. If possible, find this product's exact value. $$\cos \frac{\pi}{12}-\cos \frac{5 \pi}{12}$$
Problem 22
Verify each identity. $$\frac{\cot ^{2} t}{\csc t}=\csc t-\sin t$$
