Question

sec x + tan x = 2, find the value of cos x
1. \(1\over 3\)
2. \(3\over 4\)
3. \(1\over 2\)
4. \(\frac{4}{5}\)

Answer 1

Correct Answer - Option 4 : \(\frac{4}{5}\)

Concept:

sec2 x - tan2 x = 1

Calculation:

Given sec x + tan x = 2     ....(i)

∵ sec² x - tan² x = 1

(sec x + tan x)(sec x - tan x) = 1

2(sec x - tan x) = 1

sec x - tan x = \(1\over 2\)              ....(ii)

Adding the equation (i) and (ii)

2 sec x = 2 + \(1\over 2\)

\(\rm{2\over \cos x} = {5\over 2}\)

cos x = \(4\over 5\)