replacing even powers of sin(x) by powers of (1-cos(x)^2)

asked 2022-08-03 21:55:57 +0100

rhaynes74
31 ●4

Hi folks, I would like to force sage to take an expression like

f = cos(x)(sin(x))^2+cos(x)^3(sin(x))^5

and replace the even powers of sin(x) by powers of (1-cos(x)^2), so that the above would become

f=cos(x)(1-cos(x)^2)+cos(x)^3(1-cos(x)^2)^2*sin(x)

Any suggestions?

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answered 2022-08-03 23:17:30 +0100

Max Alekseyev

6488 ●9 ●47 ●153

One can use wildcards for this purpose:

f = cos(x)*(sin(x))^2+cos(x)^3*(sin(x))^5
w = SR.wild(0)
f.subs({sin(x)^w:((1-cos(x)^2)^floor(w/2)*sin(x)^(w-2*floor(w/2)))})

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Asked: 2022-08-03 21:55:57 +0100

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Last updated: Aug 03 '22

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replacing even powers of sin(x) by powers of (1-cos(x)^2) edit

1 Answer