If the distance between the centers of two circles of unit radii is 1 the common area of the circles is
1) `(2 pi)/(3)-sqrt(3)`
2)`(2 pi)/(3)+sqrt(3)`
3) `(2 pi)/(3)-(sqrt(3))/(2)`
4) `(2 pi)/(3)(sqrt(3))/(3)`

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

A triangle is inscribed in a circle.The vertices of the triangle divide the circle into three arcs of length 3,4 and 5 ,then the area of the triangle is equal to 1.(9sqrt(3)(1+sqrt(3)))/(pi^(2)) 2.(9sqrt(3)(sqrt(3)-1))/(pi^(2)) 3.(9sqrt(3)(1+sqrt(3)))/(2 pi^(2)) 4.(9sqrt(3)(sqrt(3)-1))/(2 pi^(2))

A pair of tangents is drawn to a unit circle with center at the origin and these tangents intersect at A enclosing an angle of 60^0 . The area enclosed by these tangents and the arc of the circle is 2/(sqrt(3))-pi/6 (b) sqrt(3)-pi/3 pi/3-(sqrt(3))/6 (d) sqrt(3)(1-pi/6)

A pair of tangents are drawn to a unit circle with centre at the origin and these tangents intersect at the point P enclosing an angle of 60^(0). The area enclosed by the tangents and the arc of the circle is,(2)/(sqrt(3))-(pi)/(6) (b) sqrt(3)-(pi)/(3)(pi)/(3)-sqrt(3)(d)sqrt(3)(1-(pi)/(6))

tan^(-1)sqrt(3)-sec^(-1)(-2)=(pi)/(3)

sin {(pi) / (3) -sin ^ (- 1) (- (sqrt (3)) / (2))}

The value of sin^(-1)(-(sqrt(3))/(2))backslash is: (A) (-pi)/(3) (B) (-2 pi)/(3)( C) (4 pi)/(3) (D) (5 pi)/(3)

Prove that (i)(1-sqrt(3)i)=2((cos)(pi)/(3)-i(sin)(pi)/(3))

Prove that (i) " sin " .(pi)/(6). " cos " .(pi)/(6) = (sqrt(3))/(4) " " (iii) cos^(2) .(pi)/(2) - sin^(2) .(pi)/(2) =(sqrt(3))/(2)

The value of (2 + sqrt(3))/(2- sqrt(3)) + (2- sqrt(3))/(2 + sqrt(3)) + ( sqrt(3) + 1)/(sqrt(3) -1) is