Question

If sec A + tan A=7, then evaluate sec A - tan A​

Answer 1

We have,

sec A + tan A = 7 ----------eqn (1)

sec A = 7 - tan A

(squaring both sides )

sec^2 A = 49 + tan^2 A - 14 tan A

sec^2 A - tan^2 A + 14 tan A - 49 = 0

( using identity sec^2 A - tan^2A = 1 )

1 + 14 tan A - 49 = 0

14 tan A = 48

tan A = 48 / 14

tan A = 24 / 7

putting in eqn (1) we will get

secA + (24 /7) = 7

we will get,

secA = 25 /7

so,

sec A - tan A = (25/7) -(24/7)

sec A - tan A = 1 / 7.

Hence

sec A - tan A = 1 / 7.

✤Another way to solve the same is✤

we have,

sec A + tan A = 7

( multiplying by sec A - tan A both sides we will get)

(sec A +tan A) (secA-tanA) = 7 ( secA-tanA)

that is

sec^2A - tan^2A = 7 ( secA-tan A)

1 = 7 ( secA - tan A)

so,

sec A - tan A = 1/7.