MHB Expression sin^n(x)/(sin^n(x)+cos^n(x))

Thread starter Vali
Start date Jan 29, 2019
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Expression

AI Thread Summary

The expression sin^n(x)/(sin^n(x)+cos^n(x)) can be simplified to 1/(cot^n(x)+1) by dividing both the numerator and denominator by sin^n(x). This transformation leads to a clearer understanding of the relationship between the two forms. The user initially struggled with this simplification but successfully grasped the concept after receiving guidance. The discussion highlights the importance of manipulating expressions in trigonometry to reveal equivalences. Ultimately, the user expressed gratitude for the assistance received.

Jan 29, 2019

Vali

Hi!
I have sin^n(x)/(sin^n(x)+cos^n(x))
The expression is the same with 1/(ctg^n(x)+1) and I have no idea how to get to this answer.
Can you help me?

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Jan 29, 2019

MarkFL

Gold Member

MHB

If you divide the numerator and denominator by \(\sin^n(x)\) what do you get?

Jan 29, 2019

Vali

1/[(sin^n(x)+cos^n(x))/sin^n(x)]
edit:
I get it.Thanks a lot! :)

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