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Explain why, if x=asecu, then a2sec2ua2is atanuif x<aand is atanuif x>a. Your explanation should include a discussion of domains and absolute values.

Short Answer

Expert verified

Ans:

Theabsolutevaluesresignificantsincetanuispositiveforuin1stquadrantandin2stquadrantitsnegativeforu.

Step by step solution

01

Step 1. Given information:

a2sec2ua2x=asecuatanux<aatanux>a

02

Step 2. Solving the trigonometric substitution:

Suppose x(-,a][a,),u0,π2π2,π, and x=asecu

x2-a2=a2sec2u-a2=a2tan2u=atanuatanu,ifx<aatanu,ifx>aTheabsolutevaluesresignificantsincetanuispositiveforuin1stquadrantandin2stquadrantitsnegativeforu.

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