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

Prove that: |a^(2)+2a2a+112a+1a+21331|=(a-1)^(3)

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

Prove that det[[a^(2)+2a,2a+1,12a+1,a+2,13,3,1]]=(a-1)^(3)

Using properties of determinants,prove that det[[a^(2)+2a,2a+1,12a+1,a+2,13,3,1]]=(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,1, 1),( 1, 1+a, 1),(1, 1, 1+a)|=a^3+3a^2

Prove that: tan^-1 +tan^-1 ((2t)/(1-t^2))=tan^-1( (3t-t^3)/(1-3t^2)), if - 1/sqrt(3),xlt 1/sqrt(3)

Prove that : tan^(-1)( (2a-b)/(bsqrt(3))) +tan^(-1)((2b-a)/(asqrt(3))) = pi/3

Evaluate the following: |[a^2+2a, 2a+1, 1],[2a+1, a+2, 1],[3,3,1]|

Prove that |1alphaalpha^2alphaalpha^2 1alpha^2 1alpha|=-(1-alpha^3)^2dot