sin[(1)/(2)cot^(-1)((2)/(3))]= [sqrt((sq...

`sin[(1)/(2)cot^(-1)((2)/(3))]=
[sqrt((sqrt(13)-2)/(2sqrt(13)))]
[(2+sqrt(13))/(2sqrt(13))]
[(sqrt(2-sqrt(13)))/(2sqrt(13))]
[(2-sqrt(13))/(2sqrt(13))]`

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

(sqrt(7)+2sqrt(3))(sqrt(7)-2sqrt(3))

(1)/(2sqrt(5)-sqrt(3))-(2sqrt(5)+sqrt(3))/(2sqrt(5)+sqrt(3)) =

([(sqrt(2)+isqrt(3))+(sqrt(2)-isqrt(3))])/([(sqrt(3)+1sqrt(2))+(sqrt(3)-1sqrt(2))])

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

(4(sqrt(6) + sqrt(2)))/(sqrt(6) - sqrt(2)) - (2 + sqrt(3))/(2 - sqrt(3)) =

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

Show that : (1)/(3-2sqrt(2))- (1)/(2sqrt(2)-sqrt(7)) + (1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5 .

If a =( 4sqrt(6))/(sqrt(2)+sqrt(3)) then the value of (a+2sqrt(2))/(a-2sqrt(2))+(a+2sqrt(3))/(a-2sqrt(3))

Simplify: 2/(sqrt(5)+\ sqrt(3))+1/(sqrt(3)+\ sqrt(2))-3/(sqrt(5)+\ sqrt(2))