`tan^(2)((1)/(2)sin^(-1)(2)/(3))=`
(A) `(7+3sqrt(3))/(2)` (B) `(7-5sqrt(3))/(2)` (C) `(7-3sqrt(5))/(2)` (D) `(7+5sqrt(3))/(2)`

(7+3sqrt(5))/(3+sqrt(5))+(7-3sqrt(5))/(3-sqrt(5))

If x=1+(1)/(3+(1)/(2+(1)/(2+(1)/(2oo))))a sqrt((5)/(2))b*sqrt((3)/(2))csqrt((7)/(3))d.sqrt((5)/(3))

Rationalise the denominator of each of the following. (i) (1)/(sqrt(7)) (ii) (sqrt(5))/(2sqrt(3)) (iii) (1)/(2+ sqrt(3)) (1)/(sqrt(3)) (v) (1)/((5+3sqrt(2)) (vi) (1)/(sqrt(7) - sqrt(6)) (vi) (1)/(sqrt(7) - sqrt(6)) (viii) (1+ sqrt(2))/(2-sqrt(2)) (ix) (3-2sqrt(2))/(3+2sqrt(2))

(2sqrt(7))/(sqrt(5)-sqrt(3))

(sqrt(3)-sqrt(5))(sqrt(3)+sqrt(5))/(sqrt(7)-2sqrt(5))

Evalute: (2+sqrt(3))^(7)+(2-sqrt(3))^(7)

Rationales the denominator and simplify: (sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) (ii) (5+2sqrt(3))/(7+4sqrt(3)) (iii) (1+sqrt(2))/(3-2sqrt(2)) (2sqrt(6)-sqrt(5))/(3sqrt(5)-2sqrt(6)) (v) (4sqrt(3)+5sqrt(2))/(sqrt(48)+sqrt(18)) (vi) (2sqrt(3)-sqrt(5))/(2sqrt(3)+3sqrt(3))

(sqrt(7)-sqrt(5))^3 - (sqrt(7)+sqrt(5))^3

The abscissas of point P and Q on the curve y=e^(x)+e^(-x) such that tangents at P and Q make 60^(0) with the x -axis are.ln((sqrt(3)+sqrt(7))/(7)) and 1n((sqrt(3)+sqrt(5))/(2))1n((sqrt(3)+sqrt(7))/(2)) (c) 1n((sqrt(7)-sqrt(3))/(2))+-1n((sqrt(3)+sqrt(7))/(2))

Simplify each of the following by rationalising the denominator,(1)/(5+sqrt(2)) (ii) (5+sqrt(6))/(5-sqrt(6)) (iii) (7+3sqrt(5))/(7-3sqrt(5)) (iv) (2sqrt(3)-sqrt(5))/(2sqrt(2)+3sqrt(3))