[" 73."(sqrt(3))/(4sqrt(9))a=(sqrt(3))/(2)vec evec i," piit "sqrt(1+a)+sqrt(1-a)(1)/(4 pi)(1)/(4 pi)vec e pi-],[[" (A) "sqrt(3)," (B) "(sqrt(3))/(2)," (C) "2+sqrt(3)(D)quad 2-sqrt(3)]]

3sqrt(4)+2sqrt(9)+5sqrt(4)-sqrt(1)-4sqrt(9)

16 * cos ""(pi)/(12) * cos"" (4pi)/(12) * cos"" (5pi)/(12)= A) sqrt1 B) sqrt2 C) sqrt3 D) sqrt4

cot^(-1)9+cosec^(-1)(sqrt(41))/(4)=(pi)/(4)

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

If (3 pi)/(4)<(A)/(2)<(5 pi)/(4) then -sqrt(1+sin A)+sqrt(1-sin A)=

int_0^(4/pi) (3x^2sin(1/x)-xcos(1/x))dx= (A) (8sqrt(2))/pi^3 (B) (32sqrt(2))/pi^3 (C) (24sqrt(2))/pi^3 (D) sqrt(2048)/pi^3

int_0^(4/pi) (3x^2sin(1/x)-xcos(1/x))dx= (A) (8sqrt(2))/pi^3 (B) (32sqrt(2))/pi^3 (C) (24sqrt(2))/pi^3 (D) sqrt(2048)/pi^3

Prove that (i) (1)/(3+sqrt(7)) + (1)/(sqrt(7)+sqrt(5))+(1)/(sqrt(5)+sqrt(3)) +(1)/(sqrt(3)+1)=1 (ii) (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+(1)/(sqrt(4)+sqrt(5))+(1)/(sqrt(5)+sqrt(6))+(1)/(sqrt(6)+sqrt(7)) +(1)/(sqrt(7)+sqrt(8))+(1)/(sqrt(8) + sqrt(9)) = 2

The integral int_(0)^( pi)sqrt(1+4sin^(2)((x)/(2))-4sin((x)/(2))dx) equal (1)pi-4(2)(2 pi)/(3)-4-4sqrt(3)(3)4sqrt(3)-4(4)4sqrt(3)-4-(pi)/(3)

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