Asked by Venkatesh

x×sin^3A=y , cos^3A = sinA × cosA , x×sinA= y×cosA , then prove that x^2+ y^2= 1
I have no idea
Answered by Steve
Hmmm. this condition

cos^3A = sinA × cosA

is very strange. It means that

cos^2A = sinA
1-sin^2A = sinA
sin^2A+sinA-1 = 0
sinA = 0.618
A = .66624 = 38.17°
cosA = .78618

Then the other equations are

y = .236x
.618x = .786y

and we're stuck.

Ya got me.
Answered by Reiny
Steve, I worked on this for a while this morning, and I got that far as well.

I also noticed that
sinA = .618033989..
which is the decimal part of the golden ratio (1+√5)/2, ... interesting

from xsinA= ycosA
I had y/x = sinA/cosA = tanA
from xsin^3A=y
I had y/x = sin^3 A

so sin^3 A = tanA
but our A of 38.17° does not satisfy this equation

it was then that I gave up.
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