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