`cos(2x)(2cos(x) + 1) = 0` Solve the equation.

Textbook Question

Chapter 5, 5.3 - Problem 22 - Precalculus (3rd Edition, Ron Larson).
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gsarora17 | (Level 2) Associate Educator

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`cos(2x)(2cos(x)+1)=0`

solving each part,

cos(2x)=0

General solutions for cos(2x)=0 are,

`2x=pi/2+2pin , (3pi)/2+2pin`

`x=(pi+4pin)/4 , (3pi+4pin)/4`

Solving 2cos(x)+1=0,

`2cos(x)=-1`

`cos(x)=-1/2`

General solutions for cos(x)=-1/2 are,

`x=(2pi)/3+2pin , (4pi)/3+2pin`

So the solutions are,

`x=(2pi)/3+2pin , (pi+4pin)/4 , (3pi+4pin)/4 , (4pi)/3+2pin`

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