+0

# Let $A,$ $B,$ $C$ be the angles of a triangle.

0
54
1
+467

Let a,b,c   be the angles of a triangle. Evaluate$$\begin{vmatrix} \sin^2 A & \cot A & 1 \\ \sin^2 B & \cot B & 1 \\ \sin^2 C & \cot C & 1 \end{vmatrix}.$$

Nov 19, 2020

#1
0

Expanding along the third column, we find that most terms cancel, and we are left with a determinant of 1.

Nov 19, 2020