If the function f(x)=⎧⎪⎪⎪⎨⎪⎪⎪⎩x+a2√2sin x,0≤x<π4xcotx+b,π4≤x≤π2b sin 2x−a cos 2x,π2<x≤π is continuous in the interval [0,π] Then the values of (a, b) are I. (-1, -1) II. (0, 0) III. (-1, 1) IV. (1, 1)

If the function f(x)=⎧⎪⎪⎪⎨⎪⎪⎪⎩x+a2√2sin x,0≤x<π

1.	If the function f(x)=⎧⎪⎪⎪⎨⎪⎪⎪⎩x+a2√2sin x,0≤x<π4xcotx+b,π4≤x≤π2b sin 2x−a cos 2x,π2<x≤π is continuous in the interval [0,π] Then the values of (a, b) are I. (-1, -1) II. (0, 0) III. (-1, 1) IV. (1, 1)
Answer» If the function $f (x) = ⎧ ⎪⎪⎪ ⎨ ⎪⎪⎪ ⎩ \begin{matrix} x + a^{2} \sqrt{2} s i n x, & 0 \leq x < \frac{π}{4} x c o t x + b, & \frac{π}{4} \leq x \leq \frac{π}{2} b s i n 2 x - a c o s 2 x, & \frac{π}{2} < x \leq π \end{matrix}$ is continuous in the interval $[0, π]$ Then the values of (a, b) are I. (-1, -1) II. (0, 0) III. (-1, 1) IV. (1, 1)