How do you prove that #sec(pi/3)tan(pi/3)=2sqrt(3)#?

1 Answer
Feb 1, 2015

You can start by breaking down your left side of the identity calculating each trigonometric function and see what happens.
Remember that #pi/3=60°# and this is a "special" angle which has "known" values of #sin, cos, tan,...# etc.

Now:

#sec(pi/3)=1/(cos(pi/3))=1/(1/2)#
#tan(pi/3)=sin(pi/3)/(cos(pi/3))=(sqrt(3)/2)/(1/2)#
Let's put them all together:
#sec(pi/3)tan(pi/3)=1/(1/2)*(sqrt(3)/2)/(1/2)=#
manipulate your fractions to get:
#=4*sqrt(3)/2=2sqrt(3)#
Which is indeed the result you needed to get to satisfy the identity.

Hope it helps