How can I rewrite sin^3(x)+\csc^3(x)? If m=\sin x +\csc x compute: R=\sin^3

Teddy Dillard

Teddy Dillard

Answered question

2022-01-14

How can I rewrite sin3(x)+csc3(x)?
If m=sinx+cscx compute:
R=sin3x+csc3x
how can I rewrite this expression

Answer & Explanation

Joseph Fair

Joseph Fair

Beginner2022-01-18Added 34 answers

Hint:
(y+1y)3=y3+1y3+3(y+1y)
RizerMix

RizerMix

Expert2022-01-20Added 656 answers

Let a=sinx b=cscx Use a3+b3=(a+b)33ab(a+b) R=m33m
alenahelenash

alenahelenash

Expert2022-01-23Added 556 answers

You also can use the factorisation a3+b3=(a+b)(a2ab+b2) so here, taking into account that sinxcscx=1, w obtain sin3x+csc3x=(sinx+cscx)(sin2x1+csc2x) =m((sinx+cscx)221)=m(m23)

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