Trigonometry in Algebra 3

Algebra Level 4

x(1+y2)(1+z2)1+x2+y(1+z2)(1+x2)1+y2+z(1+x2)(1+y2)1+z2 x \sqrt{ \dfrac{(1+y^2)(1+z^2)}{1+x^2}} + y \sqrt{ \dfrac{(1+z^2)(1+x^2)}{1+y^2}} + z \sqrt{ \dfrac{(1+x^2)(1+y^2)}{1+z^2}}

Given that x,yx,y and zz are positive reals satisfying xy+xz+yz=1xy + xz + yz = 1, evaluate the expression above.


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