Exercises 20.1, page 541

(Note: “Answers” to trigonometric identities are intermediate steps of suggested reductions of the left member.)

1. $\sin x = \frac{\tan x}{\sec x} = \frac{\frac{\sin x}{\cos x}}{\frac{1}{\cos x}} = \frac{\sin x}{\cos x} \cdot \frac{\cos x}{1} = \sin x$
3. $0.7813 = \frac{0.6157}{0.7880}$
5. ${(- \frac{1}{2} \sqrt{3})}^{2} + {(- \frac{1}{2})}^{2} = \frac{3}{4} + \frac{1}{4} = 1$
7. $\sin x - 1$
9. $\cot θ - 2 \cos θ$
11. $\sec^{2} u$
13. $\tan x \sec x$
15. $\sin t \cos t$
17. $\cot^{2} y (\csc^{2} y + 1)$
19. $\frac{\sin x}{\frac{\sin x}{\cos x}} = \frac{\sin x}{1} (\frac{\cos x}{\sin x})$
21. $\sin x (\frac{1}{\cos x})$
23. $\csc^{2} x (\sin^{2} x)$
25. $\sin x (\csc^{2} x) = (\sin x) (\csc x) (\csc x) = \sin x (\frac{1}{\sin x}) \csc x$
27. $\cos θ (\frac{\cos θ}{\sin θ}) + \sin θ = \frac{\cos^{2} θ + \sin^{2} θ}{\sin θ} = \frac{1}{\sin θ}$
29. $\cot θ (\sec^{2} θ - 1) = \cot θ \tan^{2} θ = (\cot θ \tan θ) \tan θ$
31. $\frac{\sin x}{\cos x} + \frac{\cos x}{\sin x} = \frac{\sin^{2} x + \cos^{2} x}{\cos x \sin x} = \frac{1}{\cos x \sin x}$
33. $(1 - \sin^{2} x) - \sin^{2} x$
35. $\frac{\sin θ}{\frac{1}{\sin θ}} +$

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