x+2sqrt(a)nx=(pi)/(2),quad x in[0,2 pi]

The function f(x)={x+a sqrt(2)sin x,0<=x<=(pi)/(4) and 2x cot x+b,(pi)/(4)<=x<=(pi)/(2) and a cos2x-b sin x,(pi)/(2), is continuous for 0<=x<=pi ,then value of a,b are

If cos (pi/12) = (sqrt(2) + sqrt(6))/(4) , then all x in (0,pi/2) such that (sqrt(3)-1)/(sin x) + (sqrt(3)+1)/(cos x) = 4sqrt(2) , then find x.

If cos (pi/12) = (sqrt(2) + sqrt(6))/(4) , then all x in (0,pi/2) such that (sqrt(3)-1)/(sin x) + (sqrt(3)+1)/(cos x) = 4sqrt(2) , then find x.

The value of F(x)=6cos x sqrt(1+tan^(2)x)+2sin x sqrt(1+cot^(2)x) where x in(0,2 pi)-{pi,(pi)/(2),(3 pi)/(2)} may be

If (dy)/(dx) +y sec x=tan x," then (sqrt(2) +1) y((pi)/(4)) - y(0)=, (A) sqrt(2) - (pi)/(4) (B) sqrt(2) + (pi)/(4) (C) sqrt(2) - (pi)/(2) (D) sqrt(2) + (pi)/(2)

If int_ (0)^(oo) e^(-x^(2)) dx = (sqrt (pi))/(2), and int_ (0)^(oo) e^(-ax^(2) ) dx, a> 0 is (i) (sqrt (pi))/(2) (ii) (sqrt (pi))/(2a) (iii) 2 (sqrt (pi))/(a) (iv) (1)/(2) sqrt ((pi)/(a))

f(x)={x+sqrt(2)a sin x,0

If int_(0)^(oo)e^(-x^(2))dx=(sqrt(pi))/(2), then int_(0)^(oo)e^(-ax^(2))dx where a>0 is: (A)(sqrt(pi))/(2) (B) (sqrt(pi))/(2a)(C)2(sqrt(pi))/(a) (D) (1)/(2)(sqrt((pi)/(a)))

If f(x)={(x+a sqrt(2) sinx"," ,0 lt x lt (pi)/(4)),(2x cotx+b",",(pi)/(4) le x le (pi)/(2)),(a cos 2x-b sinx",", (pi)/(2) lt x le pi):} is continuous at x=(pi)/(4) , then a - b is equal to