Use Pythagorean Identities to find tan θ if sec θ = 4√3/5 and csc θ <0

Question

use pythagorean identities to find tan

Answer 1

If sec = 4sqrt(3)/5, then cos = 5/(4sqrt(3))

cos^2 + sin^2 = 1

25/48 + sin^2 = 1

sin^2 = 23/48

sin = sqrt(23)/(4sqrt(3)

tan = sin/cos = sqrt(23)/5