Given: f (x) = tan–1(sin X + cos X)
To show: the given function is increasing in 0, π/4 .
Explanation: Given f (x) = tan–1(sin X + cos X)
Applying first derivative with respect to x, we get
Expanding (sin x+cos x )2, we get
But sin2x+cos2x = 1 and 2sin Xcos X = sin2x, so the above equation becomes,
Now for f(x) to be decreasing function,
f’(x)≥0