Question

tan²x+secx=5 , then sec x=​

Answer 1

Answer:

Given that sec x + tan x = 5, or

1+sin x = 5 cos x

Consider a right angled triangle ABC, with AB as the adjacent and BC as the opposite and AC as the hypotenuse and <A = x.

So sec x + tan x = 5, or

sec A + tan A = 5, or

AC/AB + BC/AB = 5, or

AC+BC = 5AB, or

AC = 5AB-BC

AB^2+BC^2=AC^2 = [5AB-BC]^2 = 25AB^2–10AB.BC+BC^2, or

AB^2 = 25AB^2–10AB.BC, or

AB = 25AB-10BC, or

24AB = 10BC, or

12AB = 5BC, or

BC/AB = 12/5 or tan A = 12/5

Hence sec A = 5–12/5= 13/5.

sec x = 13/5.

The RAT has a base of 5 units, opposite of 12 units and a hypotenuse of 13 units.