trigonometry

Soarer · **Posted:** Sat, 24 May 2003 16:12:02 UTC

Let x=sinA, y=sinB, z=sin(A+B). Express cos(A+B) in the form of the quotient of two polynomials with integral coefficients in x,y, and z.

bugzpodder · **Joined:** Sun, 4 May 2003 16:04:19 UTC **Posts:** 2906

Soarer · **Posted:** Sat, 24 May 2003 18:39:18 UTC

cool...
I doubt that there's enough space for me to write this answer into the blank, lol~

helmut · **Posted:** Sat, 24 May 2003 19:32:58 UTC

bugzpodder:
It looks nicer if you put a "\" in front of the trig functions, eg. "\sin A".
$\sin(A+B)=\sin A\cos B+\cos A\sin B\\ =x\cos B+y\cos A\\ z^2=x^2\cos^2 A+y^2\cos^2 B+2xy\cos A\cos B\\ z^2-x^2(1-x^2)-y^2(1-y^2)=2xy\cos A\cos B\\ \cos A\cos B=\frac{z^2-x^2(1-x^2)-y^2(1-y^2)}{2xy}\\ \cos(A+B)=\cos A\cos B+\sin A\sin B\\ \cos(A+B)=\frac{z^2-x^2(1-x^2)-y^2(1-y^2)+2x^2y^2]}{2xy}$

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trigonometry

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