Question

Question #9ed58

Answer 1

`sec((5pi)/6)tan(-pi/6)=2/3`

Explanation:

Assuming 'x' is referring to multiplication, we will use the following:

Definitions of `sec` and `tan`:

• `sec(theta) = 1/cos(theta)`
• `tan(theta) = sin(theta)/cos(theta)`

`sin` is odd and `cos` is even:

• `sin(-theta) = -sin(theta)`
• `cos(-theta) = cos(theta)`

Well known angles:

• `sin(pi/6) = 1/2`
• `cos(pi/6) = sqrt(3)/2`
• `cos((5pi)/6) = -sqrt(3)/2`

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With those, we have

`sec((5pi)/6)tan(-pi/6) = 1/cos((5pi)/6)(sin(-pi/6)/cos(-pi/6))`

`=1/cos((5pi)/6)((-sin(pi/6))/cos(pi/6))`

`=1/(-sqrt(3)/2)((-1/2)/(sqrt(3)/2))`

`=2/3`