`int(dx)/(1+x^4)^(1/4)=1/2(1/2log(1+z)/(1-z)-tan^(- 1)z)+C` , where (A) `z= (root(4) (1+x^4))/x` (B) `z=x/ (root(4) (1+x^4))` (C) `z=- (root(4) (1+x^4))/x` (D) none of these

If int(x^2-2)/((x^4+5x^2+4)tan^-1((x^2+2)/x))dx=log|f(z)|+c , then (A) f(z)=tan^-1z , where z=sqrt(x+2) (B) f(z)=tan^-1z , where z=x+2/x (C) f(z)=sin^-1z , where z=(x+2)/x (D) none of these

If int(x^2-2)/((x^4+5x^2+4)tan^-1((x^2+2)/x))dx=log|f(z)|+c , then (A) f(z)=tan^-1z , where z=sqrt(x+2) (B) f(z)=tan^-1z , where z=x+2/x (C) f(z)=sin^-1z , where z=(x+2)/x (D) none of these

Simplify : (i) log_(1/(sqrtx) )(y) xx log_(1/(root(3)(y)))(z) xx log_(1/(root(4)(z)))(x)

If sin ^ (- 1) x + sin ^ (- 1) y + sin ^ (- 1) z = pi then x ^ (4) + y ^ (4) + z ^ (4) + 4x ^ (2) y ^ (2) z ^ (2)

If sin ^ (- 1) x + sin ^ (- 1) y + sin ^ (- 1) z = pi then x ^ (4) + y ^ (4) + z ^ (4) + 4x ^ (2) y ^ (2) z ^ (2) =

If x + y + z = xyz , prove that x(1 -y^(2)) (1- z^(2))+ y(1- z^(2))(1- x^(2)) +z(1-x^(2)) (1- y^(2)) = 4xyz .

2^(x)=4^(y)=8^(z) and (1)/(2x)+(1)/(4y)+(1)/(4z)=4

If sin ^ (- 1) x + sin ^ (- 1) y + sin ^ (- 1) z = pi, show that x ^ (4) + y ^ (4) + z ^ (4) + 4x ^ ( 2) y ^ (2) z ^ (2) = 2 (x ^ (2) y ^ (2) + y ^ (2) z ^ (2) + z ^ (2) x ^ (2))