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The value of \(\rm \frac{\cos\theta+i\sin\theta}{\cos\theta-i\sin\theta}\) is:
1. 1
2. cos 2θ - i sin 2θ
3. cos 2θ + i sin 2θ
4. None of these.

1 Answer

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Best answer
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 e.

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.

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