Question #9ed58

1 Answer
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#