Question

If tan2 θ = 2, then cos 2θ = ?
1. 1
2. \(\frac 1 2\)
3. \(\frac 1 3\)
4. \(\rm \frac {-1}{3}\)
5. None of these

Answer 1

Correct Answer - Option 4 : \(\rm \frac {-1}{3}\)

Concept:

cos 2θ = \(\rm \dfrac {1-tan^2\theta}{1+tan^2\theta}\)

Calculations:

Given, tan2 θ = 2

We know that 

cos 2θ = \(\rm \frac {1-tan^2\theta}{1+tan^2\theta}\)

⇒ cos 2θ = \(\rm \frac {1-2}{1+2}\)

⇒ cos 2θ = \(\rm \frac {-1}{3}\)

Hence, if tan2 θ = 2, then cos 2θ = \(\rm \frac {-1}{3}\)