`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))`

Simplify (sqrt(13)-sqrt(11))/(sqrt(13)+sqrt(11)) + (sqrt(13)+sqrt(11))/(sqrt(13)-sqrt(11))

Comparison of ratios (sqrt(13))/(sqrt(8)),(sqrt(17))/(sqrt(15))

sqrt(13^(2))-sqrt(36) times sqrt(4)=

sqrt((13)^(4))=?

lim_(x rarr1)(13sqrt(x)-7sqrt(x))/(5sqrt(x)-3sqrt(x))

Two circles, each having radius 4, have a common tangent given by 3x+2y-6=0 at (2, 0) . Then their centres are : (A) (2+ 5/sqrt(13), 8/sqrt(13)), (2- 5/sqrt(13) , (-8)/sqrt(13)) (B) (2+ 12/sqrt(13), 8/sqrt(13)) , (2- 12/sqrt(13), (-8)/sqrt(13)) (C) (2, 3), (4, 5) (D) none of these

cos^(-1)((3cosx-2sinx)/(sqrt(13)))

(13+2sqrt(5))^(2)=?sqrt(5)+189

1/(sqrt7+sqrt6-sqrt13)=

If x=sqrt(7)-sqrt(5) and y=sqrt(13)-sqrt(11) then