Re: Simple, but a bit hard, Trigonometry problem.

In news:<46588a88@xxxxxxxxxxxxx> schrieb Thomas Mautsch <mautsch@xxxxxxx>:
In news:<1180007573.461047.82770@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
schrieb gtsavdar@xxxxxxxxx <gtsavdar@xxxxxxxxx>:
[ ... ]
If:
a = Sin(5 degrees)
b = Sin(49 degrees)
c = Sin(87 degrees)

then prove that:
Sin(73 degrees) = (a^2 - b^2 + a c) / ( 4 a (a^2 - b^2 + a c) - (a-b+c) )
[ ... ]

I have the feeling that maybe I mixed up a sign or two.
So here is the argument again, this time in Maple code:

a := sin(5): b:=sin(49): c:= sin(180-87):
( a*(a+c)/b - b ) / (4*a*( a*(a+c)/b-b ) - ( (a+c)/b -1 ));
eval(%,c=-a+2*b*cos(44));
eval(%,2*a*cos(44)=combine(2*a*cos(44)));
combine(%);
numer(%)*sin(73)/combine(denom(%)*sin(73));
eval(%,107=180-107);

[Note: Don't be bothered by the degrees vs. radians issue. ;-)]

Result:


/sin(5) (sin(5) + sin(93)) \ / /
|------------------------- - sin(49)| / |
\ sin(49) / / \

/sin(5) (sin(5) + sin(93)) \
4 sin(5) |------------------------- - sin(49)|
\ sin(49) /

sin(5) + sin(93) \
- ---------------- + 1|
sin(49) /

2 sin(5) cos(44) - sin(49)
= -----------------------------------------------------
4 sin(5) (2 sin(5) cos(44) - sin(49)) - 2 cos(44) + 1


sin(39)
= - ---------------------------------
-4 sin(5) sin(39) - 2 cos(44) + 1


sin(39)
= -------------
2 cos(34) - 1


sin(39) sin(73)
= ----------------------------
sin(107) + sin(39) - sin(73)


= sin(73)

q.e.d.



.

Quantcast