Solve for A: cos 9A = (cos 15A)(cos 8A)

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- Sep 8th 2009, 11:30 PMpacmantrigonometric equation
Solve for A: cos 9A = (cos 15A)(cos 8A)

- Sep 8th 2009, 11:58 PMpacman
i have tried to use a math program, and the graph looks like this, the red dot are the roots. I think there so many of them

- Sep 9th 2009, 01:45 AMGrandad
Hello pacmanI can't see how to find the complete solution yet, but the most likely approach is probably to use on the RHS and say:

Now use on each side:

or

So that, at least, gives some solutions:

But what happens next with the remaining expression, I'm not sure. You could use and then remove the factor from both sides to get:

(which doesn't give any more answers that we haven't already got from ), or:

which you*could*then express simply in terms of , but it would be pretty horrendous!

Grandad - Sep 9th 2009, 04:26 AMdhiab
**Hello this is the solution :**

- Sep 9th 2009, 04:32 AMGrandad
- Sep 9th 2009, 05:41 AMpacman
**dhiab**, this puzzled me,

http://www.mathhelpforum.com/math-he...828d72bc-1.gif

a is not 20 degrees or what, as GRANDAD have said your post sems puzzling.

But THANKS though, it cracks my mind

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(Headbang) - Sep 9th 2009, 07:34 AMpacmanMathematica gave this factorization, but i can not arrive to it, please help.

32 sin^2(A) sin(A-pi/4) sin(2A-pi/4) sin(A+pi/4) sin(2A+pi/4) cos(A) (2cos(2A)-1) (2cos(6A)+4 cos(8A)+4 cos(10A)+2 cos(12A)+1) = 0 - Sep 9th 2009, 07:36 AMpacman
a few more plot of the said equation,