If a `ne`0 and a`ne`1, show that
`|{:(x+1,x,x),(x,x+a,x),(x,x,x+a^(2)):}|=a^(3)[1+x((a^(3)-1))/(a^(2)(a-1))].`

If |{:(x,-6,-1),(2,-3x,x-3),(-3,2x,x+2):}|=0 then x = ……..

If |{:(x,e^(x-1),(x-1)^(3)),(x-lnx,cos(x-1),(x-1)^(2)),(tanx,sin^(2)x,cos^(2)x):}|=a_(0)+a_(1)(x-1)+a_(2)(x-1)^(2)cdots The value of cos^(-1) (a_(1)) is

If |{:(1,x,x^(2)),(x,x^(2),1),(x^(2),1,x):}| =3 then the value of |{:(x^(3)-1,0,x-x^(4)),(0,x-x^(4),x^(3)-1),(x-x^(4),x^(3)-1,0):}| is

Prove that, tan^(-1)x+"tan"^(-1)(2x)/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2))),|x|lt1/sqrt3

Show that 1/(x+1)+5/(x^2+1)+4/x^4+1)+…..+2^n/(x^2^n+1)= /(x-1)- 2^(n+1)/(x^2(n+1) -1)

If |{:(x+1,x-1),(x-3,x+2):}|=|{:(4,-1),(1,3):}| then find x

Find the sum of (x + (1)/(x))^(2), (x^(2) + (1)/(x^(2)))^(2), (x^(3) + (1)/(x^(3)))^(2) , ……..to n terms

If f(x)=|{:(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x^2-1)):}| then f(100)= ………

If a gt 0 and a ne 1, 2 log_(x)a +log_(ax)a +3 log_(a^(2)x) a = 0 , then x =