Question #9ed58

1 Answer
sente
Dec 21, 2016

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

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

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