Let theta = x
as mod is there
func will behave in same way as if x was in first quadrant.
we get sin x + cosx
= root 2 . sin ( pi/4 + x )
diff. and equate to 0 find x for which value is max... we get root 2 as max
and for minimum value .. root2. sin ( pi/4 + x) and , so, sin( pi/4 + x) should be minimum...with x E [0 , pi/2]
draw graph of sin ( pi / 4 + x) by shifting graph of sinx to left by pi/4 units... and in interval of x E [0, pi/2] we see that minimum value is when x = 0
which gives minimum value as 1...
range is from 1 to root 2
f(x) E [1, root2]
NOW
when greatest integer function is applied..
we get range as
1
PLZ RATE :)
