A linear Algebra Problem (3x3 Matrix)

1. Jan 31, 2013

timelyrainsun

1. The problem statement, all variables and given/known data
I want to proove the determinant of the following 3x3 matrix is 0.

1 1 1

tanA tanB tanC

tan2A tan2B tan2C

where A+B+C=2pi.

2. Relevant equations

Sorry I don't know how to type here so I show in the attachment.

3. The attempt at a solution

Sorry I have attempted but found no way closed to the solution.

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Last edited: Jan 31, 2013
2. Jan 31, 2013

HallsofIvy

Staff Emeritus
If you want to do it then you first have to attempt to do it and you have shown no attempt. Under "relevant equations" you might put something like
$$\left|\begin{array}{ccc}a & b & c \\ d & e & f \\ g & h & i\end{array}\right|= a\left|\begin{array}{cc}e & f \\ h & i\end{array}\right|- b\left|\begin{array}{cc}d & f \\ g & i\end{array}\right|+ c\left|\begin{array}{cc}d & e \\ g & h\end{array}\right|$$
as well as some trig identities like
$$tan(2A)= \frac{2tan(A)}{1+ tan^2(A)}$$

Last edited: Jan 31, 2013
3. Jan 31, 2013

timelyrainsun

f
Sorry it is my bad. Thanks!

Last edited by a moderator: Jan 31, 2013
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