Mathematica Expand cos^5t in Mathematica: Guide & Steps

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To expand cos^5(t) in Mathematica, the command "expand" is not effective. Instead, using "TrigReduce[Cos[x]^5]" will yield the expression in terms of first-degree sine and cosine functions. The result is cos^5(t) expressed as (10cos(t) + 5cos(3t) + cos(5t))/16. This method provides a useful way to simplify trigonometric expressions in Mathematica. Understanding these commands enhances the ability to manipulate trigonometric functions effectively.
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How can I tell Mathematica to expand cos^5 t?

The command expand doesn't do it.
 
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dwsmith said:
How can I tell Mathematica to expand cos^5 t?

The command expand doesn't do it.

Are you trying to write it in first degree terms of sine and cosine? If so, expand isn't the command to do this and I don't know off the top of my head if there is one that would do such a thing.
 
Is
$$\cos^{5}(t)=\frac{10\cos(t)+5\cos(3t)+\cos(5t)}{16}$$
helpful?
 
Ackbach said:
Is
$$\cos^{5}(t)=\frac{10\cos(t)+5\cos(3t)+\cos(5t)}{16}$$
helpful?

I learned something new today; I didn't realize that this was an option in Mathematica. The command:

Code:
TrigReduce[Cos[x]^5]

outputs what Ackbach posted above.
 

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