Correct Answer - Option 3 : cos 2θ + i sin 2θ
Concept:
Euler's formula:
A complex number z = cos θ + i sin θ can also be written as eiθ.
Calculation:
From the Euler's formula, we know that:
\(\rm \frac{\cos\theta+i\sin\theta}{\cos\theta-i\sin\theta}=\frac{e^{i\theta}}{e^{-i\theta}}\) = e2iθ = cos 2θ + i sin 2θ.