Shoe that `((-1+sqrt(- 3))/2)^(19)+((-1-sqrt(- 3))/2)^(19)=-1`

Show that , ((-1+sqrt(-3))/(2))^(19)+((-1-sqrt(-3))/(2))^(19)=-1.

Prove that: sin^(-1)((3)/(5))+cos^(-1)((5)/(sqrt(26)))=tan^(-1)((19)/(17))

Prove that : (1)/(sqrt(2)+1)+ (1)/(sqrt(3)+sqrt(2))+ (1)/(2+sqrt(3))=1

((2+sqrt(3))/2)/(1+(sqrt(3)+1)/2) + ((2-sqrt(3))/2)/(1-((sqrt(3)-1)/2))

If sqrt(2) = 1.414, sqrt(3) = 1.732, sqrt(5) = 2.236 and sqrt(6) = 2.449 , find the value of (2+sqrt(3))/(2-sqrt(3)) +(2-sqrt(3))/(2+sqrt(3)) +(sqrt(3) -1)/(sqrt(3) +1)

(-sqrt(3)/2 + sqrt(3))/(1/sqrt(2)-1)=

The value of (2 + sqrt(3))/(2- sqrt(3)) + (2- sqrt(3))/(2 + sqrt(3)) + ( sqrt(3) + 1)/(sqrt(3) -1) is

(3)/(sqrt(19-2sqrt(88)))-(8)/(sqrt(14+2sqrt(33)))=