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

Dear Student

Cos A function in terms of sec A: sec A = 1/cos A

⇒cos A = 1/sec A
sec A function in terms of sec A:

cos^2 A + sin^2 A = 1 Rearrange the terms

sin^2 A = 1 - cos^2 A
sin^2 A = 1 - (1/sec^2 A)

sin^2 A = (sec^2 A-1)/sec^2 A
sin A = ± √(sec^2 A-1)/sec A

cosec A function in terms of sec A: sin A = 1/cosec A

⇒cosec A = 1/sin A
cosec A = ±sec A/√(sec^2 A-1)

Now,
tan A function in terms of sec A:
sec^2 A - tan^2 A = 1
Rearrange the terms
⇒tan^2 A = sec^2 A – 1

tan A = √(sec^2 A - 1)

cot A function in terms of sec A:
tan A = 1/cot A

⇒cot A = 1/tan A
cot A = ±1/√(sec^2 A + 1)

Thanks