If the function f(x)=⎧⎪
⎪⎨⎪
⎪⎩x+a2√2sin x,0≤x<π4x cot x+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
since f is continuous at x = π4
∴f(π4)−fh→0(π4+h)−fh→0(π4−h)
⇒π4cotπ4+b−fh→0(π4+h)+a2√2sin(π4+h)
⇒π4(1)+b−(π4+0)+a2√2 sin(π4+0)
⇒π4+b−π4+a2√2 sinπ4
⇒b−a2√21√2⇒b−a2
Also as f is continuous at x - π4
∴f(π2)=limx→π2−0f(x)=limx→−0f(π2−h)
⇒b sin 2π2−a cos 2π2=limh→−0[(π2−h)cot(π2−h)+b]
⇒b.0−a(−1)=0+b⇒a=b
Hence (0,0) satisfy the above relations.