If the function f ( x ) , defined below is continuous in the interval [ 0 , π ] , then_____ 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

Step-by-step solution

Given that 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 f x is continuous in 0 ,   π If f x is continuous in a , b that means it should be continuous at all points in a , b . lim x → π 4 f x = f π 4 ⇒ π 4 + a = π 2 + b ⇒ a - b =   π 4 - - - - ( I ) lim x → π 2 f x = f π 2 &#865