If a ,b,c are real numbers such that `0 lt a lt 1,0 lt b lt 1, 0 lt c, lt 1, ` a+b+c=2 then prove that `(a)/(1-a) , (b)/(1-b) . (c )/(1-c) gt= 8`.

The set of all real numbers satisfying the inequality X - 2 lt 1 is

If r is a real number such that |r|lt1 and if a=5(1-r) , then a) 0ltalphalt5 b) -5ltalt5 c) 0ltalt10 d) 0lealt10

The equation a cos theta + b sin theta = c has a solution when a,b and c are real numbers such that : a) a lt b lt c b) a = b=c c) c ^(2) lea ^(2) + b ^(2) d) c ^(2) le a ^(2) -b ^(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 b ne c and |[a , a^2, 1+a^3],[ b, b^2, 1+b^3],[ c, c^2, 1+ c^3]| =0 then prove that a b c =-1

If x lt 0 , then prove that cos^(-1)x=pi+tan^(-1)""(sqrt(1-x^2))/x

If (b-c)^(2) , (c-a)^(2), (a-b)^(2) are in A.P. then prove that (1)/(b-c) , (1)/(c-a), (1)/(a-b) are also in A.P.