Prove that
`((3)/(2)+(1)/(sqrt(2)))((3)/(2)-(1)/(sqrt(2)))=(7)/(4)`

Prove that (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+....+(1)/(sqrt(8)+sqrt(9))=2

(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))

Prove that (i) (1)/(3+sqrt(7)) + (1)/(sqrt(7)+sqrt(5))+(1)/(sqrt(5)+sqrt(3)) +(1)/(sqrt(3)+1)=1 (ii) (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+(1)/(sqrt(4)+sqrt(5))+(1)/(sqrt(5)+sqrt(6))+(1)/(sqrt(6)+sqrt(7)) +(1)/(sqrt(7)+sqrt(8))+(1)/(sqrt(8) + sqrt(9)) = 2

The value of 6+log_((3)/(2))((1)/(3sqrt(2))sqrt(4-(1)/(3sqrt(2))sqrt(4-(1)/(3sqrt(2))sqrt(4-(1)/(3sqrt(2))...cdots))))

Prove that 4+5(-(1)/(2)+(i sqrt(3))/(2))^(334)+3(-(1)/(2)+(i sqrt(3))/(2))^(335)=i sqrt(3)

Prove that sin ((23pi)/24) = sqrt((2 sqrt2 - sqrt3 -1)/(4 sqrt2))

The value of 6+log_((3)/(2))((1)/(3sqrt(2))sqrt(4-(1)/(3sqrt(2))sqrt(4-...))

Prove that: sin15^(@)=(sqrt(3)-1)/(2sqrt(2))

Prove that: sin15^(@)=(sqrt(3)-1)/(2sqrt(2))

Prove that: 1/(1+sqrt(2))+1/(sqrt(2)+sqrt(3))+1/(sqrt(3)+sqrt(4))+1/(sqrt(4)+sqrt(5))+1/(sqrt(5)+sqrt(6))+1/(sqrt(6)+sqrt(7))+1/(sqrt(7)+sqrt(8))+1/(sqrt(8)+sqrt(9)) = 2