Question

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

Answer 1

`"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"`