Answer :

Taking LHS,

Firstly, multiply and divide R1, R2, R3 by x, y, z respectively, we get



[rearrange the terms]


Taking xyz common from the first and second column, we get




Applying C3 C3 + C1, we get



Taking common (xy + yz + xz) common from C3, we get



If any two columns (or rows) of a determinant are identical (all corresponding elements are same), then the value of determinant is zero.


Here, C2 and C3 are identical.


Hence,


LHS = RHS


Hence Proved


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