Question

Sec A+Tan A =1/3,What is Sec A – Tan A ?

Answer 1

sec A + tan A = 1/3
sec A - tan A = (?)

Now,
sec² A - tan² A = 1
∴(sec A + tan A) (sec A - tan A) = 1   [∵a² - b² = (a+b)(a-b) ]
∴1/3 *(sec A - tan A) = 1
∴sec A - tan A = 1* 3
∴sec A - tan A = 3

Answer 2

sec A + tan A = 1/3
sec A - tan A = unknown

So,
sec² A - tan² A = 1
∴  (sec A + tan A) (sec A - tan A) = 1 
∴  1/3 *(sec A - tan A) = 1

∴  sec A - tan A = 3