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Chapter 7: Q. 80 (page 465)

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

sec胃=tan胃+cot胃

Short Answer

Expert verified

The solution set of the given equation is蟺2.

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

localid="1647016175573" sec胃=tan胃+cot胃

02

Step 2. The equation in its present form contains a secant, cotangent and tangent.

We know thatsec胃=1cos胃,tan胃=sin胃cos胃,cot胃=cos胃sin胃

03

Step 3. Putting the value in the given equation.

sec胃=tan胃+cot胃1cos胃=sin胃cos胃+cos胃sin胃

The LCD is role="math" localid="1647016289932" cos胃路sin胃.

04

Step 4. Multiply with the LCD on both side.

1cos胃路cos胃路sin胃=sin胃cos胃路cos胃路sin胃+cos胃sin胃路cos胃路sin胃sin胃=sin胃路sin胃+cos胃路cos胃sin胃=sin2胃+cos2胃

05

Step 5. We know that sin2θ+cos2θ=1

So sin胃=1

Solving each equation in the interval [0,2蟺], we obtain

胃=蟺2

So the solution set is蟺2.

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Most popular questions from this chapter

Establish each identity.

1+sin胃+cos胃1+sin胃-cos胃=1+cos胃sin胃

True or False:sin-胃+cos-胃=cos胃-sin胃

Establish each identity.

tan胃+cot胃=sec胃csc胃

Establish each identity.

1-2cos2胃sin胃cos胃=tan胃-cot胃

solve each equation on the interval

0鈮�胃<2蟺

sin胃+cos胃=2
See all solutions

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