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In Problems 64-75, solve each equation on the interval0≤θ<2π

Short Answer

Expert verified

The solution set isθ∈0,π6,5π6

Step by step solution

01

Given information

Given expressionsin(2θ)-cosθ-2sinθ+1=0

02

Checking the value lie in the specific interval

Calculating, we get

sin(2θ)-cosθ-2sinθ+1=02sinθcosθ-cosθ-2sinθ+1=02sinθ(cosθ-1)-(cosθ-1)=0(cosθ-1)(2sinθ-1)=0cosθ-1=0cosθ=12sinθ-1=02sinθ=1sinθ=12θ∈0,π6,5π6

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