If the function f x = x + a 2  sin x 0 ≤ x < π 4 2 x cot x + b     π 4 ≤ x ≤ π 2 a cos  2 x - b sin x   π 2 < x ≤ π is continuous in 0 ,  π , then the values of a and b respectively are

Step-by-step solution

∵     f x is continuous in 0 ,  π so it is continuous at x = π 4    and   x = π 2 ∴     lim x → π 4 - f x = lim x → π 4 + f x ⇒     π 4 + a = π 2 + b .....(1) and    lim x → π 2 - f x = lim x → π 2 + f x ⇒    0 + b = - a - b .....(2) By solving (1) and (2), we get,      a = π 6 ,  b = -