求助，证明行列式等式

为便于手打、排版，令sinα=A、sinβ=B、sinγ=C、cosα=X、cosβ=Y、cosγ=Z
行列式=|AX+AX AY+BX AZ+CX|
BX+AY BY+BY BZ+CY
CX+AZ CY+BZ CZ+CZ
=|AX AY AZ|+|AX AY CX|+|AX BX AZ|+|AX BX CX|+|AX AY AZ|+|AX AY CX|+|AX BX AZ|+0
BX BY BZ BX BY CY BX BY BZ BX BY CY AY BY BZ AY AY CY AY BY BZ
CX CY CZ CX CY CZ CX BZ CZ CX BZ CZ AZ CY CZ AZ CY CZ AZ BZ CZ
【第8个行列式为：|AX BX CX|
=0+0+0+0+0+0+0+0 AY BY CY
=0 AZ BZ CZ 】

【解释：d1∵c1/c2=x/y；d2∵c1/c2=x/y；d3∵c1/c3=x/z；d4∵c2/c3=b/c；d5∵c2/c3=y/z；
d6∵c1/c3=a/c；d7∵c1/c2=a/b；d8∵r1/r2=x/y
若提出公因子，很容易看出两列（或两行）相等的情形！】