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博文33908's Question
Math
Posted about 2 months ago
可以詳細的化簡過程
Cos^3化簡
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Answer from Sia
Posted about 2 months ago
Solution by Steps
step 1
We start by simplifying cos3(x)\cos^3(x)
step 2
Using the trigonometric identity, we have: cos3(x)=14(3cos(x)+cos(3x))\cos^3(x) = \frac{1}{4} (3 \cos(x) + \cos(3x))
step 3
Another way to express cos3(x)\cos^3(x) is using the exponential form: cos3(x)=18(eix+eix)3\cos^3(x) = \frac{1}{8} (e^{-ix} + e^{ix})^3
Answer
cos3(x)=14(3cos(x)+cos(3x))\cos^3(x) = \frac{1}{4} (3 \cos(x) + \cos(3x)) or cos3(x)=18(eix+eix)3\cos^3(x) = \frac{1}{8} (e^{-ix} + e^{ix})^3
Key Concept
Simplification of cos3(x)\cos^3(x) using trigonometric identities and exponential form
Explanation
The simplification of cos3(x)\cos^3(x) can be achieved using trigonometric identities or by expressing it in terms of exponential functions. Both methods provide equivalent results.

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