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Chapter 7: Q. 43 (page 501)

Solve each equation on the interval0鈮�胃鈮�2蟺

role="math" localid="1646548318952" sin鈦�(2胃)+sin鈦�(4胃)

Short Answer

Expert verified

0,蟺3,蟺2,2蟺3,4蟺3,5蟺3,蟺

Step by step solution

01

Step 1. Given information 

We have been given sin鈦�(2胃)+sin鈦�(4胃).

We have to establish identity.

02

Step 2. Simplify the expression

We know,

sin(4胃)=sin(2路2胃)

sin(2x)=2sin(x)cos(x)

Therefore, we get

role="math" localid="1646548778688" sin鈦�(2胃)+sin鈦�(4胃)=0sin鈦�(2胃)+2sin鈦�(2胃)cos鈦�(2胃)=0sin鈦�(2胃)(1+2cos鈦�(2胃))=0

03

Step 3. Solve for each expression

Solve for sin(2胃)

Suppose x=2胃

Therefore,

sin(x)=0

To get zero x must be role="math" localid="1646548747327" 0,蟺2,蟺,3蟺2......

Now solve for role="math" localid="1646548919161" 1+2cos鈦�(2胃)

Suppose x=2胃

Therefore,

1+2cos(x)=0cos(x)=-12

For this x must be equal to 2蟺3+k蟺or4蟺3+办蟺

Hence,

胃 is equal to0,蟺3,蟺2,2蟺3,4蟺3,5蟺3,蟺

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