[tan[(1)/(2)cos^(-1)((sqrt(2))/(3))]=],[[" (a) "(3-sqrt(5))/(2)," (b) "(3+sqrt(5))/(2)],[" (c) "(2)/(3-sqrt(5))," (d) "(2)/(3+sqrt(5))]]

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)

(1)/(2+sqrt(3))+(2)/(sqrt(5)-sqrt(3))+(1)/(2-sqrt(5))=0

The value of cos48cos12 (A) (sqrt(5)+3)/(8) (B) (3-sqrt(5))/(2) (C) (sqrt(5)+1)/(4) (D) (sqrt(5)-1)/(4)

Find the direction cosines of the line which is perpendicular to the lines with direction ratios 4, 1, 3 and 2, -3, 1 . a) (1)/(sqrt(3)),(1)/(5sqrt(3)),(-7)/(5sqrt(3)) b) (5)/(sqrt(3)),(1)/(sqrt(3)),(7)/(5) c) (2)/(sqrt(3)),(5)/(2sqrt(3)),(1)/(7sqrt(3)) d) (1)/(sqrt(3)),(2)/(sqrt(3)),(-1)/(sqrt(3))

(((3+sqrt(5))/2)^2+1+((3-sqrt(5))/2)^2)/(((3+sqrt(5))/2)^2-1+((3-sqrt(5))/2)^2)

Find ( sqrt(5) + 1 )/( sqrt(5 ) - 1) = ( A ) ( 3 + sqrt(5) )/2 ( A ) ( 3 - sqrt(5) )/2 ( A ) ( 3 + sqrt(5) )/4 ( A ) ( 3 - sqrt(5) )/4

If angle between the lines (x-2)/(1)=(y-3)/(2)=(z+5)/(-2) and 2x-y-kz=lambda is cos^(-1)((2sqrt(2))/(3)) then find k( A) sqrt((3)/(5))(B)(3)/(sqrt(5))(C)(sqrt(5))/(3)(D)sqrt((5)/(3))

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

The domain of f(x)=sin^(-1)[2x^(2)-3], where [.] denotes the greatest integer function,is (-sqrt((3)/(2)),sqrt((3)/(2)))uu(-sqrt((5)/(2)),sqrt((5)/(2)))(-sqrt((3)/(2)),-1)uu(-sqrt((5)/(2)),-1)uu(1,sqrt((5)/(2)))(-sqrt((5)/(2)),sqrt((5)/(2)))(-sqrt((5)/(2)),-1)uu(1,sqrt((5)/(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))