Show that `4sin27^0=(5+sqrt(5))^(1/2)-(3-sqrt(5))^(1/2)`

The value of alpha such that sin^(-1)2/(sqrt(5)),sin^(-1)3/(sqrt(10)),sin^(-1)alpha are the angles of a triangle is (-1)/(sqrt(2)) (b) 1/2 (c) 1/(sqrt(3)) (d) 1/(sqrt(2))

Show that ((sqrt(3))/(2) + (i)/(2))^(5) + ((sqrt(3))/(2) - (i)/(2))^(5) = -sqrt(3)

Solve sqrt(5)x^(2) + x + sqrt(5)=0

Which of the following is the value of sin 27^0-cos 27^0? (a) -(sqrt(3-sqrt(5)))/2 (b) (sqrt(5-sqrt(5)))/2 (c) -(sqrt(5)-1)/(2sqrt(2)) (d) none of these

Tangent of acute angle between the curves y=|x^2-1| and y=sqrt(7-x^2) at their points of intersection is (5sqrt(3))/2 (b) (3sqrt(5))/2 (5sqrt(3))/4 (d) (3sqrt(5))/4

If the tangent drawn at point (t^2,2t) on the parabola y^2=4x is the same as the normal drawn at point (sqrt(5)costheta,2sintheta) on the ellipse 4x^2+5y^2=20, then theta=cos^(-1)(-1/(sqrt(5))) (b) theta=cos^(-1)(1/(sqrt(5))) t=-2/(sqrt(5)) (d) t=-1/(sqrt(5))

The number of terms in the expansion of (1 + 5sqrt(2)x)^(9) + (1 - 5sqrt(2)x)^(9) is

The number of solutions of the equation sqrt(x^(2))-sqrt((x-1)^(2))+sqrt((x-2)^(2))=sqrt(5) is

Let S be the set of all non-zero real numbers such that the quadratic equation alphax^2-x+alpha=0 has two distinct real roots x_1a n dx_2 satisfying the inequality |x_1-x_2|<1. Which of the following intervals is (are) a subset (s) of S ? (1/2,1/(sqrt(5))) b. (1/(sqrt(5)),0) c. (0,1/(sqrt(5))) d. (1/(sqrt(5)),1/2)