`frac{sqrt 3+ sqrt 4}{sqrt 3 - sqrt 4}`

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

Simplify : (\sqrt 5 - \sqrt 3)/(\sqrt 3 + \sqrt 5) \times (\sqrt 5 - \sqrt 3)/(\sqrt 3 -\sqrt 5)

Simplify {(\sqrt 5+\sqrt 3)\times (\sqrt 5 - \sqrt 3)}/(\sqrt 7- \sqrt 3)\times (\sqrt 7+ \sqrt 3)/(\sqrt 7+\sqrt 3)

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

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

Find (sqrt3 - sqrt 2)/(sqrt 3+sqrt 2) -(sqrt3 + sqrt 2)/(sqrt 3-sqrt 2) +1/(sqrt2+1)-1/(sqrt2-1)

Simplify: 1/(sqrt5 + sqrt4) + 1/(sqrt4 + sqrt3) + 1/(sqrt3 + sqrt2) + 1/(sqrt2 + sqrt1)

Simplify: (\sqrt 5+\sqrt 3)/(\sqrt 5 - \sqrt 3)\times (\sqrt 5+\sqrt 3)/(\sqrt 5 +\sqrt 3)

The centre of an ellipse is at origin and its major axis coincides with x-axis. The length of minor axis is equal to distance between foci and passes through the point (sqrt29, 2sqrt(29/5)) , then which of the following points lie on ellipse (A) (4sqrt3, 2sqrt2) (B) (4sqrt3, 2sqrt3) (C) (4sqrt2, 2sqrt3) (D) (4sqrt2, 2sqrt2)