Exercises 20.3, page 549

1. $- \sqrt{3}$
3. $- \frac{24}{25}$
5.

$\begin{array}{l} \sin 60 ° = \sin 2 (30 °) = 2 \sin 30 ° \cos 30 ° \\ = 2 (\frac{1}{2}) (\frac{1}{2} \sqrt{3}) = \frac{1}{2} \sqrt{3} \end{array}$
7. $\tan 120 ° = \frac{2 \tan 60 °}{1 - \tan^{2} 60 °} = \frac{2 \sqrt{3}}{1 - {(\sqrt{3})}^{2}} = - \sqrt{3}$
9. $\sin 100 ° = 2 \sin 50 ° \cos 50 ° = 0.9848$
11. $\cos 96 ° = \cos^{2} 48 ° - \sin^{2} 48 ° = - 0.1045285$
13.

$\begin{array}{l} \tan \frac{2 π}{7} & = \frac{2 \tan \frac{π}{7}}{1 - \tan^{2} \frac{π}{7}} \\ = 1.254 \end{array}$
15. $\frac{24}{25}$
17. $- \sqrt{3}$
19. $3 \sin 10 x$
21. $\cos 8 x$
23. $\cos x$
25. $- 4 \cos 4 x$
27. $2 \sin 3 θ$
29. 2
31. $\cos^{2} α - (1 - \cos^{2} α)$
33. $\frac{\cos x - (\sin x / \cos x) \sin x}{1 / \cos x} = \cos^{2} x - \sin^{2} x$
35. $\frac{2 \sin θ \cos θ}{1 + 2 \cos^{2} θ - 1} = \frac{\sin θ}{\cos θ}$
37. $1 - (1 - 2 \sin^{2} 2 θ) = \frac{2}{\csc^{2} θ}$
39. $\ln \frac{1 - \cos 2 x}{1 + \cos 2 x} = \ln \frac{2 \sin^{2} x}{2 \cos^{2} x} = {\ln tan}^{2} x$
41.
43.

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Basic Technical Mathematics, 11th Edition by Allyn J. Washington, Richard Evans