Prove that : `|a^2 2a+1 1 2a+1a+2 1 3 3 1|=(a-1)^3`

Prove that: |a^2+2a2a+1 1 2a+1a+2 1 3 3 1|=(a-1)^3 .

Using properties of determinants, prove that 3 2 (a 1) 3 3 1 2a 1 a 2 1 a 2a 2a

Prove that |[a^2+2a,2a+1,1],[2a+1,a+2,1],[3,3,1]|=(a-1)^3

Using properties of determinants, prove that |(a^2+2a, 2a+1,1), (2a+1, a+2, 1), (3,3,1)| = (a-1)^3

Using properties of determinants, prove that |(a^2+2a, 2a+1,1), (2a+1, a+2, 1), (3,3,1)| = (a-1)^3

Using properties of determinant, prove that |{:(a^(2)+2a, 2a+1, 1), (2a+1, a+2, 1), (3, 3, 1):}|=(a-1)^(3)

Prove that : tan^(-1) 1 + tan^(-1) 2 + tan^(-1) 3= pi = 2(tan^(-1) 1 + tan^(-1)((1)/(2)) + tan^(-1)( (1)/(3)))

Prove: |(1,a, a^2),(a^2, 1,a),( a, a^2, 1)|=(a^3-1)^2

Prove that : tan^(-1)2+tan^(-1)3=(3pi)/4

Prove that : tan^(-1)2+tan^(-1)3=(3pi)/4