Question

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

Answer 1

SecA+tanA=1/3 //as we know....sec^2A-tan^2A=1 //(SecA-tanA)(SecA+tanA)=1 //(secA-tanA)(1/3)=1 //SecA-tanA=3

Answer 2

we know the trigonometric identity: sec² A- Tan²A =1
this can be written as (secA - tanA)(secA +tanA) =1  since a²+b² = (a+b)(a-b)
let this be eq(1)
given, (secA+tanA)=1/3
by substituting in the above eq(1)
we get,
(1/3)(secA-tanA) =1
secA -tanA = 1/(1/3)
⇒sec A - tan A = 3