The Student Room Group
Reply 1
What in the world is the magic triangle?
Reply 2
Use the angles pi/4 and pi/6.
Not sure what a magic triangle is...you shouldn't need to resort to any magic to solve this one.
Reply 3
I meant the triangles where you can easily read the cos,sines of etc in surd form..
sorry, I dont quite understand your hint with the pi/4 pi/6 idea?
thanks again
Reply 4
Well, cos2A = 2cos²A - 1.

Let A = 5pi/12.

cos(5pi/6) = 2cos²(5pi/12) - 1.

Can you take it from here?
Reply 5
http://artpad.art.com/?jjfhnudcxw

That's the triangle. Dunno if it's your magic one.
But you're looking to find the lengths cosAcosB and sinAsinB.

[edit]
Well, fine. If you're going to do it the normal way, you might as well just say
5/12 = 1/4+1/6 and cos(A+B) = cosAcosB-sinAsinB.

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