Q3 of 256 Page 7

Evaluate the following:

Applying, C₂→C₂ + C₁

Taking, (a + b + c) common,

Applying R₂→R₂ – R₁, and R₃→R₃ – R₁

Taking, (b – c) and (c – a) common,

= (a + b + c)(b – a)(c – a)(b – c)

So, Δ = (a + b + c)(b – a)(c – a)(b – c)

Without expanding, show that the value of each of the following determinants is zero:

, where A, B, C are the angles of ΔABC.

Evaluate the following: