Expert: Paul Klarreich - 9/17/2009

Question
Can you help me to solve this out?

tan ( sec^-1 (8) ) = ?

I know we should put a logarithm somewhere but i am not sure how to solve this! Can you explain how to do it please?

Answer
Questioner: Alvin
Country: United States
Category: Advanced Math
Private: No
Subject: help me with trigonometry
Question: Can you help me to solve this out?

tan ( sec^-1 (8) ) = ?

I know we should put a logarithm somewhere

>> You do?  I don't.

but i am not sure how to solve this! Can you explain how to do it please?
........................................
tan (arcsec(8))

The key is to remember that  arcsec() or arc-anything, IS AN ANGLE.

So write  

A = arcsec(8), and you have to find tan(A)

Then sec A = 8.

Now you memorized (What? You didn't?  Then do it!) that:

tan^2(A) = sec^2(A) - 1

So

tan^2(A) = 8^2 - 1 = 63

and

tan A = sqrt(63)

That's it.  No logarithms.