`((2-sqrt(2))(2+sqrt(2)))/(4-2sqrt(2))`

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

Prove the following statements.sin7((1)/(2))^(@)=(sqrt(4-sqrt(6)-sqrt(2)))/(2sqrt(2))

(sqrt(2)+sqrt(2)+sqrt(2))/(sqrt(2))

(4+sqrt(2))/(2+sqrt(2))=a-sqrt(b)

(sqrt(2)+sqrt(2)-sqrt(2))/(sqrt(2))=?

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

The value of the integral int_0^(3/2) [x^2]dx , where [] denotes the greatest integer function, is (A) 2+sqrt(2) (B) 2-sqrt(2) (C) 4+2sqrt(2) (D) 4-2sqrt(2)

If 0 < x < pi/2 , intsqrt(1+secx)dx=2sin^(-1)(asin^(-1)(x/b))+C , where C is arbitrary constant, then ordered pair (a , b) is (1,sqrt(2)) (2) (sqrt(2),1) (sqrt(2),2) (4) (2,sqrt(2))

Simplify (i) (4+ sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (ii) (1)/(sqrt(3) + sqrt(2)) - (2)/(sqrt(5)-sqrt(3)) -(2)/(sqrt(2) - sqrt(5)) (iii) (2+sqrt(3))/(2-sqrt(3)) + (2-sqrt(3))/(2+sqrt(3)) + (sqrt(3)-1)/(sqrt(3)+1) (iv) (2+sqrt(6))/(sqrt(2)+sqrt(3))+(6sqrt(2))/(sqrt(6)+sqrt(3)) -(8sqrt(3))/(sqrt(6)+sqrt(2))