Write all the other trigonometric ratios of ∠A in terms of secA.

We know, cosA = 1/secA
We know, sin²A + cos²A = 1
sin²A = 1 - cos²A
sinA = √(1 - (1/secA)²) = √(sec²A - 1)/secA
We know, cosec A = 1/sinA
∴ cosec A = secA/√(sec²A - 1)
We know, cotA = cosA/sinA = (1/secA) / (√(sec²A - 1)/secA)
∴ cotA = 1/√(sec²A - 1)
We know, tanA = 1/cotA
∴ tanA = √(sec²A - 1)