Q 58. Complete the proof of Theorem 9.... [FREE SOLUTION]

Chapter 9: Q 58. (page 757)

Complete the proof of Theorem 9.14 by verifying that
${(f' (胃) \cos 胃 - f (胃) \sin 胃)}^{2} + {(f' (胃) \sin 胃 + f (胃) \cos 胃)}^{2}$ is equal to ${(f' (胃))}^{2} + {(f (胃))}^{2}$

Short Answer

Expert verified

It is proved that ${(f' (胃) \cos 胃 - f (胃) \sin 胃)}^{2} + {(f' (胃) \sin 胃 + f (胃) \cos 胃)}^{2} = {(f' (胃))}^{2} + {(f (胃))}^{2}$

Step by step solution

Step 1. Given information

Left side of the equation is ${(f' (胃) \cos 胃 - f (胃) \sin 胃)}^{2} + {(f' (胃) \sin 胃 + f (胃) \cos 胃)}^{2}$

Step 2. Explanation

$\begin{array}{rcl} {(f' (胃) \cos 胃 - f (胃) \sin 胃)}^{2} + {(f' (胃) \sin 胃 + f (胃) \cos 胃)}^{2} & = & {(f' (胃))}^{2} (\cos^{2} 胃 + \sin^{2} 胃) - 2 f' (胃) f (胃) \cos 胃 \sin 胃 + {(f (胃))}^{2} (\sin^{2} 胃 + \cos^{2} 胃) \\ + 2 f' (胃) f (胃) \cos 胃 \sin 胃 \\ = & {(f' (胃))}^{2} + {(f (胃))}^{2} \end{array}$

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91影视

Complete the proof of Theorem 9.14 by verifying that
${(f' (胃) \cos 胃 - f (胃) \sin 胃)}^{2} + {(f' (胃) \sin 胃 + f (胃) \cos 胃)}^{2}$ is equal to ${(f' (胃))}^{2} + {(f (胃))}^{2}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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91影视

Complete the proof of Theorem 9.14 by verifying thatf'胃cos胃-f胃sin胃2+f'胃sin胃+f胃cos胃2is equal tof'胃2+f胃2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Geometry

Statistics

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

Complete the proof of Theorem 9.14 by verifying that
${(f' (胃) \cos 胃 - f (胃) \sin 胃)}^{2} + {(f' (胃) \sin 胃 + f (胃) \cos 胃)}^{2}$ is equal to ${(f' (胃))}^{2} + {(f (胃))}^{2}$