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Chapter 7: Q. 72 (page 496)

In Problems 69-78, solve each equation on the interval 0鈮�胃<2蟺.

sin2胃=cos胃.

Short Answer

Expert verified

The solution set for the equationsin2胃=cos胃is,蟺6,蟺2,5蟺6,3蟺2.

Step by step solution

01

Step 1 Given equation is,

sin2胃=cos胃.

The double angle formula for sin2胃is sin2胃=2sin胃cos胃.

Substitute the known values in the given equation.

2sin胃cos胃=cos胃2sin胃cos胃-cos胃=0cos胃2sin胃-1=0cos胃=0or2sin胃-1=02sin胃=1sin胃=12

02

Step 2 Solving each equation in the interval [0,2π),

胃=蟺6胃=蟺2胃=5蟺6胃=3蟺2

Hence the solution set is,蟺6,蟺2,5蟺6,3蟺2.

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