`(2sin^2 (x) - 1)(tan^2 (x) - 3) = 0` Solve the equation.

Textbook Question

Chapter 5, 5.3 - Problem 24 - Precalculus (3rd Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Solve the equation `(2sin^2(x)-1)(tan^2(x)-3)=0`

Set each factor equal to zero and solve for the x values.

`2sin^2(x)-1=0`

`2sin^2(x)=1`

`sin^2(x)=1/2`

`sin(x)=+-sqrt(1/2)`

`sin(x)=+-sqrt(2)/2`

`x=pi/4+pi/2n`

`tan^2(x)-3=0`

`tan^2(x)=3`

`tan(x)=+-sqrt(3)`

`x=pi/3+pin`

`x=(2pi)/3+pin` 

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