Question

If tan θ - sec θ = 2, then find the value of cot θ ?
1. 1/4
2. 5/7
3. 3/4
4. 4/3

Answer 1

Correct Answer - Option 4 : 4/3

Concept:

Some useful formulas are,

sec2 θ - tan2 θ = 1

tan θ = \(\rm 1\over \cot θ\)

Calculation:

We know that, 

sec² θ - tan² θ = 1; which can be written as,

(sec θ + tan θ)(sec θ - tan θ) = 1

Since, (tan θ - sec θ) = 2      ....(1)

We can write the above equation as,

⇒ (sec θ + tan θ) = - \(1\over 2\)         ...(2)

By adding eq(1) and eq(2) we get,

2 tan θ = 2 - \(\rm 1\over 2\) = \(\rm 3\over 2\)

⇒ tan θ = \(\rm 3\over 4\)

⇒ cot θ = \(\rm 4\over 3\)