`1/(1+z^(a-b)+z^(a-c)).1/(1+z^(b-c)+z^(b-a)).1/(1+z^(c-a)+z^(c-b))` would reduce to

If a ,\ b ,\ c >0\ a n d\ x ,\ y ,\ z in R , then the determinant |\ \ (a^x+a^x)^2(a^x-a^(-x))^2 1(b^y+b^(-y))^2(b^y-b^(-y))^2 1(c^z+c^(-z))^2(c^z-c^(-z))^2 1| is equal to- a. a^x b^y c^x b. a^(-x)b^(-y)c^(-z)\ c. a^(2x)b^(2y)c^(2x) d. zero

Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|= |(1+a x)^2(1+b x)^2(1+c x)^2(1+a y)^2(1+b y)^2(1+c y)^2(1+a z)^2(1+b z)^2(1+c z)^2|=2(b-c)(c-c)(a-b)xx(y-z)(z-x)(x-y)dot

Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|= |(1+a x)^2(1+b x)^2(1+c x)^2(1+a y)^2(1+b y)^2(1+c y)^2(1+a z)^2(1+b z)^2(1+c z)^2|= 2(b-c)(c-c)(a-b)xx(y-z)(z-x)(x-y)dot

Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|= |(1+a x)^2(1+b x)^2(1+c x)^2(1+a y)^2(1+b y)^2(1+c y)^2(1+a z)^2(1+b z)^2(1+c z)^2|=2(b-c)(c-c)(a-b)xx(y-z)(z-x)(x-y)dot

Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|= |(1+a x)^2(1+b x)^2(1+c x)^2(1+a y)^2(1+b y)^2(1+c y)^2(1+a z)^2(1+b z)^2(1+c z)^2|=2(b-c)(c-c)(a-b)xx(y-z)(z-x)(x-y)dot

If a,b,c gt 0 and x,y,z , in R then the determinant : |((a^x+a^(-x))^2,(a^(x)-a^(-x))^2,1),((b^y+a^(-y))^2,(b^(y)-b^(-y))^2,1),((c^z+c^(-z))^2,(c^(z)-c^(-z))^2,1)| is equal to :

If x=(a-b)/(a+b), y=(b-c)/(b+c) and z=(c-a)/(c+a) , find the value of ((1+x)(1+y)(1+z))/((1-x)(1-y)(1-z))

If z(1+a)=b+i c and a^2+b^2+c^2=1, then [(1+i z)//(1-i z)= A. (a+i b)/(1+c) B. (b-i c)/(1+a) C. (a+i c)/(1+b) D. none of these

If z_(1),z_(2),z_(3) are three distinct non-zero complex numbers and a,b,c in R^(+) such that (a)/(|z_(1)-z_(3)|)=(b)/(|z_(2)-z_(3)|)=(c)/(|z_(3)-z_(1)|),quad then (a^(2))/(z_(1)-z_(2))+(b^(2))/(z_(2)-z_(3))+(c^(2))/(z_(2)-z_(1)) is equal to Re(z_(1)+z_(2)+z_(3))( b) Im g(z_(1)+z_(2)+z_(3))0(d) None of these