sin(b)*sin(a+(1/2)*b) = sin(a)*sin((1/2)*a+b)=sin(b+a)*cos((a-b)*(1/2))
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From: Robert Israel on 13 Aug 2010 17:14 "M.A.Fajjal" <h2maf(a)yahoo.com> writes: > How many exact possible solution for > > sin(b)*sin(a+(1/2)*b) = sin(a)*sin((1/2)*a+b)=sin(b+a)*cos((a-b)*(1/2)) > > The solutions are not important. But the number of solutions > > How to confirm this number Infinitely many, of course, since (a=0,b=0) is a solution and the expressions are all periodic in a and b with period 4 pi. Or did you want the number of solutions in, say, [0, 4 pi) x [0, 4 pi) ? I think I counted 24 (graphically). -- Robert Israel israel(a)math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada |