Solution:

In terms of sec A, the cos A function:

sec A = 1/cos A

⇒ cos A = 1/sec A

Now write, sec A function in terms of sec A:

cos²A + sin²A = 1

Rearranging the above given terms

sin²A = 1 – cos²A

sin²A = 1 – (1/sec²A)

sin²A = (sec²A-1)/sec²A

sin A = ± √(sec²A-1)/sec A

In terms of sec A cosec A function:

sin A = 1/cosec A

⇒cosec A = 1/sin A

cosec A = ± sec A/√(sec²A-1)

Now write, in terms of sec A tan A function:

sec²A – tan²A = 1

Rearranging the above given terms

⇒ tan²A = sec²A – 1

tan A = √(sec²A – 1)

In terms of sec A cot A function:

tan A = 1/cot A

⇒ cot A = 1/tan A

cot A = ±1/√(sec²A – 1)