If `sqrtab= sqrta sqrtb and a lt 0`, then find arg `(b+ai)`

If |a| lt 1 and |b| lt 1 then the sum of the series 1+(1+a) b+(1+a+ a^(2))b^(2)+ (1+a+a^(2)+a^(3)) b^(3)+cdots is

Let A and B be two events such that P (A uu B) = P (A) + P (B) - P (A) P (B).If 0 lt P (A) lt 1 and 0 lt P (B) lt1, then P (A uuB)' is equal to

If tan alpha = (b)/(a) , a gt b gt 0 and if 0 lt alpha lt (pi)/(4) , then sqrt((a+b)/(a-b)) - sqrt((a-b)/(a+b)) is equal to

If 0 lt x lt (pi)/(2) , then find tan ((pi)/(4)+ (x)/(2) ) + tan ((pi)/(4) - (x)/(2) )

If a and b are positive numbers such that a gt b , then the minimum value of a sec theta- b tan theta (0 lt theta lt pi/2) is a) 1/sqrt(a^2-b^2) b) 1/sqrt(a^2+b^2) c) sqrt(a^2+b^2) d) sqrt(a^2-b^2)

If y = tan^(-1)(1/2)+tan^(-1)b , (0 lt blt 1) and 0 lt y le pi/4 , then the maximum value of b is a) 1//2 b) 1//3 c) 1//4 d) 2//3