Let `f(x)={(sinx+cosx",",0 lt x lt (pi)/(2)),(a",",x=pi//2),(tan^(2)x+"cosec"x",",pi//2 lt x lt pi):}`
Then its odd extension is

Let f(x) = {:{( sin x +cos x, 0 lt x lt (pi)/(2) ),( a, x = pi//2) , ( tan ^(2) x + cosecx , pi//2lt xlt pi ):} then its odd extension is

The value of a and b such that the function f(x)={(-2sinx"," , -pi le x le -(pi)/(2)),(a sinx+b",", -(pi)/(2) lt x lt (pi)/(2)),(cosx",", (pi)/(2) le x le pi ):} is continuous in [-pi,pi] are

If f(x)={:{((sin 2x)/(sqrt(1-cos 2x))", for " 0 lt x lt pi/2),((cos x)/(pi-2x)", for " pi/2 lt x lt pi):} , then

If f(x)={:{((sin 2x)/(sqrt(1-cos 2x))", for " 0 lt x lt pi/2),((cos x)/(pi-2x)", for " pi/2 lt x lt pi):} , then

f(x) = {{:(xsinx " if " 0 ltx le(pi)/(2)),((pi)/(2)sin(pi + x )" if " (pi)/(2) lt x lt pi):} then f(x) is discontinuous at

If f(x)={:{(x sin x", for " 0 lt x le pi/2),(pi/2 sin (pi+x)", for " pi/2 lt x lt pi):} , then

If f(x)={:{(x sin x", for " 0 lt x le pi/2),(pi/2 sin (pi+x)", for " pi/2 lt x lt pi):} , then

If f(x)={:{((sin2x)/(sqrt(1-cos2x))", for " 0 lt x le pi/2),((cos x)/(pi-2x)", for "pi/2 lt x le pi):}

If f(x)={(x+a sqrt(2) sinx"," ,0 lt x lt (pi)/(4)),(2x cotx+b",",(pi)/(4) le x le (pi)/(2)),(a cos 2x-b sinx",", (pi)/(2) lt x le pi):} is continuous at x=(pi)/(4) , then a - b is equal to

Lt_(x to (pi)/(2))[ sinx]=