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juan01sebastian00
04.12.2019 •
Mathematics
Use euler's formula to derive the identity. (note that if a, b, c, d are real numbers, a + bi = c + di means that a = c and b = d. simplify your answer completely.) sin(2θ) = 2 sin(θ) cos(θ) using euler's formula, we have ei(2θ) = + i sin(2θ). on the other hand, ei(2θ) = (eiθ)2 = + i sin(θ) 2 = (cos2(θ) − sin2(θ)) + i sin(θ) . equating correct: your answer is correct. parts, we find sin(2θ) = 2 sin(θ) cos(θ).
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Ответ:
Answer with Step-by-step explanation:
We have to prove that
Euler's formula :![e^{i\theta}=cos\theta+isin\theta](/tpl/images/0402/3584/356d0.png)
By using Euler's identity, we get
Comparing imaginary part on both sides
Then, we get
Hence, proved.
Ответ: