ChristopherW28
How do you factor sin^3x + cos^3x?



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myininaya
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Do you know how to factor a sum of cubes?

myininaya
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There is a cute formula for it.

myininaya
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\[a^3+b^3=(a+b)(a^2ab+b^2)\]

ChristopherW28
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Looks cute lol thank you

myininaya
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lol. Do you know how to use it with the trig functions?

myininaya
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\[(\sin(x))^3+(\cos(x))^3=a^3+b^3 \]

myininaya
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should be easy for you to determine what is a and what is b.

myininaya
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if it isn't then let me know so i can explain further

ChristopherW28
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I've got the equation down but what to do first?

ChristopherW28
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Do I multiply what's in the parenthesis?

myininaya
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no

myininaya
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tell me what a is and what b is based on what I wrote above

ChristopherW28
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A is sin and b is cos

myininaya
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\[(\sin(x))^3+(\cos(x))^3=a^3+b^3 \]

myininaya
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ok so just go to the other side of the formula and replace a with sin(x) and replace b with cos(x)
and then you are done
don't do nothing more

ChristopherW28
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I did :)

myininaya
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ok then you are done sir

myininaya
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\[a^3+b^3=(a+b)(a^2ab+b^2) \]
everywhere we seen an a we put sin(x)
everywhere we seen a b we put cos(x)

ChristopherW28
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Thanks!

myininaya
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np :)

ChristopherW28
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I will have another question in a moment

myininaya
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k