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Chapter 7: Q. 61 (page 465)

In Problems 57鈥� 80, solve each equation on the interval 0鈮�胃鈮�2蟺

(tan胃-1)(sec胃-1)=0

Short Answer

Expert verified

The solution set of the given equation is0,蟺4,5蟺4

Step by step solution

01

Step 1. Given Information 

In the given problems we have to solve each equation on the interval 0鈮�胃鈮�2蟺.

(tan胃-1)(sec胃-1)=0

02

Step 2. The equation in its present form contains a tangent and secant. Use the Zero-Product Property. 

tan胃-1=0or蝉别肠胃-1=0迟补苍胃-1=0+1or蝉别肠胃-1+1=0+1迟补苍胃=1or蝉别肠胃=1

03

Step 4. Solving each equation in the interval [0,2π), we obtain 

胃=蟺4,5蟺4or胃=0

So the solution set is0,蟺4,5蟺4

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Most popular questions from this chapter

A rectangle is inscribed in a semicircle of radius 1. See the illustration.

Part (a): Express the area A of the rectangle as a function of the angle 胃shown in the illustration.

Part (b): Show that A胃=sin2胃.

Part (c): Find the angle 胃 that results in the largest area A.

Part (d): Find the dimensions of this largest rectangle.

cos-胃-cos胃

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