Question

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

Answer 1

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