`sqrt(2+sqrt(2+sqrt(2+sqrt(2+sqrt2))))=`
(A) `cos(pi/32)`
(B) `2cos(pi/32)`
(C) `2cos(pi/64)`
(D) `cos(pi/64)`

Let alpha = tan^-1 (1/2)+tan^-1(1/3) , beta=cos^-1(2/3)+cos^-1(sqrt5/3) , gamma=sin^-1(sin((2pi)/3))+1/2cos^-1(cos((2pi)/3)) The value of cos(alpha+beta+gamma) is equal to (A) cos((5pi)/12) (B) cos ((7pi)/12) (C) -cos(pi/12) (D) -cos ((7pi)/12)

lim_(xrarr1^(-)) (sqrtpi-sqrt(2sin^-1x))/sqrt(1-x)= (A) sqrt(2/pi) (B) sqrt(pi/2) (C) 1/pi (D) sqrt(1/pi)

sin^-1 (cos(sin^-1(sqrt(3)/2))= (A) pi/3 (B) pi/6 (C) - pi/6 (D) none of these

The value of cos^(-1)sqrt(2/3)-cos^(-1)((sqrt(6)+1)/(2sqrt(3))) is equal to (A) pi/3 (B) pi/4 (C) pi/2 (D) pi/6

cos(pi/65)cos((2pi)/65)cos((4pi)/65)cos((8pi)/65)cos((16pi)/65)cos((32pi)/64)=1/64

Range of the function f(x)=sqrt(cos^(- 1)(sqrt(log_4x))-pi/2)+sin^(- 1)((1+x^2)/(4x)) is equal to (A) (0,pi/2+sqrt(pi/2)] (B) [pi/2,pi/2+sqrt(pi/2)] (C) [pi/6,pi/4) (D) {pi/6}

Range of the function f(x)=sqrt(cos^(- 1)(sqrt(log_4x))-pi/2)+sin^(- 1)((1+x^2)/(4x)) is equal to (A) (0,pi/2+sqrt(pi/2)] (B) [pi/2,pi/2+sqrt(pi/2)] (C) [pi/6,pi/4) (D) {pi/6}

sin^(-1)sqrt((2-sqrt(3))/4)+cos^(-1)(sqrt(12)/4)+sec^(-1)(sqrt(2))= (a) 0 (b) pi/4 (c) pi/6 (d) pi/2

Prove that: cos(pi/4+A)+cos(pi/4-A)=sqrt(2)cosA

If A(3/sqrt(2), sqrt(2)) , B(-3/sqrt(2), sqrt(2)), C(-3/sqrt(2), -sqrt(2)) and D(3 cos theta , 2 sin theta) are four points . If the area of the quadrilateral ABCD is maximum where theta in (3 pi/2, 2 pi) then (a) maximum area is 10 sq units (b) theta = 7 pi/4 (c) theta = 2 pi- sin^(-1) 3/ sqrt(85) (d) maximum area is 12 sq units