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2026-04-04 16:12:21.1775319141
Computing a certain trigonometric determinant
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Hint
Start with $R_2'=R_2-R_1, R_3'=R_3-R_1$
$$\cot B-\cot A=\dfrac{\sin(A-B)}{\sin A\sin B}$$
Using Prove $ \sin(A+B)\sin(A-B)=\sin^2A-\sin^2B $
$$\sin^2B-\sin^2A=-\sin(A+B)\sin(A-B)$$
Finally $A+B=\pi-C$