Prove that `sqrt(x^(-1)y).sqrt(y^(-1)z).sqrt(z^(-1)x)=1`

Prove that sqrt(x^(-1)y)xxsqrt(y^(-1)z)xxsqrt(z^(-1)x)=1

If x,y,z are positive real numbers show that: sqrt(x^(-1)y)*sqrt(y^(-1)z)*sqrt(z^(-1)x)=1

Prove that. (i) sqrt(x^(-1) y) .sqrt(y^(-1) z) . Sqrt(z^(-1) x) = 1 (ii) ((1)/(x^(a-b)))^((1)/(a-c)).((1)/(x^(b-c))).((1)/(x^(c-b)))^((1)/(c-b))= 1 (iii) (x^(a(b-c)))/(x^(b(a-c))) div ((x^(b))/(x^(a))) (iv) ((x^(a+b))^(2)(x^(b+c))^(2)(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))

if,sin^(-1)x+sin^(-1)y+sin^(-1)z=pi then prove that x sqrt(1-x^(2))+y sqrt(1-y^(2))+z sqrt(1-z^(2))=2xyz

If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi prove that x sqrt(1-x^(2))+y sqrt(1-y^(2))+z sqrt(1-z^(2))=2xyz

If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi, prove that: x sqrt(1-x^(2))+y sqrt(1-y^(2))+z sqrt(1-z^(2))=2xyz

Show : sqrt( x^-1y) times sqrt( y^-1z ) times sqrt( z^-1x) = 1

If sin^(-1)x + sin^(-1)y + sin^(-1)z =pi , prove that xsqrt(1 - x^(2)) + y sqrt(1 -y^(2)) + z sqrt(1-z^(2))= 2xyz .

If cos^(-1)x+2sin^(-1)x+3cot^(-1)y+4tan^(-1)y=4sec^(-1)z+5cos ec^(-1)z, then prove that sqrt(z^(2)-1)=(sqrt(1+x^(2))-xy)/(x+y sqrt(1-x^(2)))