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Chapter 7: Q. 27 (page 505)

Solve each equation on 0鈮�胃<2蟺.

cos2胃+2sin胃cos胃-sin2胃=0

Short Answer

Expert verified

The solution set is胃=3蟺8,7蟺8,11蟺8,15蟺8.

Step by step solution

01

Step 1. Given Information 

We are given the equation cos2胃+2sin胃cos胃-sin2胃=0and we need to find the solutions of the equation on the interval 0鈮�胃<2蟺.

02

Step 2. Simplifying the equation 

We know,

sin2胃=2sin胃cos胃cos2胃=cos2胃-sin2胃

cos2胃+2sin胃cos胃-sin2胃=0鈬�cos2胃-sin2胃+2sin胃cos胃=0鈬�cos2胃+sin(2胃)=0鈬�sin(2胃)=-cos2胃鈬�sin(2胃)cos2胃=-cos2胃cos2胃鈬�tan2胃=-1鈬�tan2胃=tan-蟺4

03

Step 3. Finding the solutions

The general solution is given by

2胃=-蟺4+k蟺, where k is an integer.

The probable values of k are 1,2,3,4.

鈭�2胃=-蟺4+k蟺鈬�胃=-蟺8+k蟺2

When k=1,

鈭�胃=-蟺8+蟺2鈬�胃=3蟺8

when k=2,

鈭�胃=-蟺8+2蟺2鈬�胃=7蟺8

when k=3,

role="math" localid="1646494815023" 鈭�胃=-蟺8+3蟺2鈬�胃=11蟺8

when k=4,

鈭�胃=-蟺8+4蟺2鈬�胃=15蟺8

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Most popular questions from this chapter

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