How do you verify that the x values $pi/3, (5pi)/3$ are solutions to $secx-2=0$ ?

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How do you verify that the x values $pi/3, (5pi)/3$ are solutions to $secx-2=0$ ?

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Answer 1 · 2018-06-21T09:36:42

$"see explanation"$

Explanation:

$"using the "color(blue)"trigonometric identity"$

$•color(white)(x)secx=1/cosx$

$cos(pi/3)=1/2$

$cos((5pi)/3)=cos(2pi-(5pi)/3)=cos(pi/3)=1/2$

$"substitute the given values of x into the left side of the"$
$"equation and if equal to right side then they are the "$
$"solutions"$

$sec(pi/3)-2=1/cos(pi/3)-2=1/(1/2)-2=2-2=0$

$"hence "pi/3" is a solution to the equation"$

$sec((5pi)/3)-2=1/cos(pi/3)-2=2-2=0$

$"hence "(5pi)/3" is a solution to the equation"$

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How do you verify that the x values $pi/3, (5pi)/3$ are solutions to $secx-2=0$ ?

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Explanation:

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How do you verify that the x values $pi/3, (5pi)/3$ are solutions to $secx-2=0$ ?