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Chapter 5: Q. 94 (page 466)

Prove part (b) of Theorem 5.18: Forx鈭�(-鈭�,鈭�)andu鈭�(-蟺/2,蟺/2),the substitution x=atanu gives x2+a2=asecu. Your proof should include a discussion of domains and a consideration of absolute values.

Short Answer

Expert verified

It is proved.

Step by step solution

01

Step 1. Given information.

It is givenx鈭�(-鈭�,鈭�),u鈭�(-蟺/2,蟺/2)

02

Step 2. Explanation.

For x=atanu

We know, From Pythagorean Theorem,

a2tan2u+a2=a2sec2ux2+a2=a2tan2u+a2=a2sec2u=|asecu|=asecu

Hence proved.

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