(d) `sqrt6/(sqrt2+sqrt3)`

Let k be a real number such that the inequality sqrt(x-3) +sqrt(6 -x) ge k has a solution then the maximum value of k is sqrt3 (2) sqrt6 -sqrt3 (3) sqrt6 (4) sqrt6 +sqrt3

If x= ( sqrt5- sqrt3)/ ( sqrt5+ sqrt3) and y= ( sqrt5+ sqrt3)/( sqrt5- sqrt3) find the value of x^(2) + y ^(2)

Solve: (sqrt 3+ sqrt2)(sqrt2-sqrt3)

Which of the following has the maximum value unity: (a) sin^2x-cos^2x (b) (sin2x-cos2x)/sqrt2 (c) -(sin2x-cos2x)/sqrt2 (d) (sqrt(6/5))(1/sqrt(2)sinx+sqrt(3)cosx)

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

Rationlise the denominator and simplify: ( 12sqrt2)/( sqrt3+ sqrt6)

Simplify (7sqrt3)/(sqrt10+sqrt3)-(2sqrt5)/(sqrt6+sqrt5)-(3sqrt2)/(sqrt15+3sqrt2)

(i) If x = (6ab)/(a + b) , find the value of : (x + 3a)/(x - 3a) + (x + 3b)/(x - 3b) . (ii) a = (4sqrt(6))/(sqrt(2) + sqrt(3)) , find the value of : (a + 2sqrt(2))/(a - 2sqrt(2)) + (a + 2sqrt(3))/(a - 2sqrt(3)) .

Prove that cot 7 ""(1^(@))/(2) = sqrt2 + sqrt3 + sqrt4 + sqrt6 = (sqrt3 + sqrt2) (sqrt2 +1 ).

Prove that tan 7 (1^(@))/(2) = sqrt2 - sqrt3 -sqrt4 + sqrt6 = (sqrt3 - sqrt2) (sqrt2 -1).