Prove that `|{:((a+1)(a+2),a+2,1),((a+2)(a+3),a+3,1),((a+3)(a+4),a+4,1):}|=-2`

Prove that tan^(-1)""(1)/(2)+tan^(-1)""(2)/(11)=tan^(-1)""(3)/(4)

Show that {:[(4,1),(2,7)][(2,1),(3,4)] ne [(2,1),(3,4)][(4,1),(2,7)]

Prove that : {:|(1!,2!,3!),(2!,3!,4!),(3!,4!,5!)]= 4!

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

Prove that: sqrt(1/4)+(0.01)^(-1/2)-(27)^(2/3)=3/2

the value of the determinant |{:((a_(1)-b_(1))^(2),,(a_(1)-b_(2))^(2),,(a_(1)-b_(3))^(2),,(a_(1)-b_(4))^(2)),((a_(2)-b_(1))^(2),,(a_(2)-b_(2))^(2) ,,(a_(2)-b_(3))^(2),,(a_(3)-b_(4))^(2)),((a_(3)-b_(1))^(2),,(a_(3)-b_(2))^(2),,(a_(3)-b_(3))^(2),,(a_(3)-b_(4))^(2)),((a_(4)-b_(1))^(2),,(a_(4)-b_(2))^(2),,(a_(4)-b_(3))^(2),,(a_(4)-b_(4))^(2)):}| is

Prove that tan^(-1)""(1)/(4)+tan^(-1)""(2)/(9)=(1)/(2)tan^(-1)""(4)/(3)

Prove that 3cos^(-1)x=cos^(-1)(4x^(3)-3x),x in[(1)/(2),1]

Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4,4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer.