Question

In the interval |0, (π/4)|, then function f(x) = tan^–1 (sin x +  cos x) is___________

(a) Decreasing 

(b) Increasing 

(c) Both 

(d) Even Function

Answer 1

The correct option (b) Increasing

Explanation:

f(x) = tan^–1 (sin x + cos x)

f'(x) = [(cos x – sin x) / (1 + (sin x + cos x)²)]

f'(x) = [{√2 cos {x + (π/4)}} / {1 + (sin x + cos x)²}]

f(x) is increasing if – (π/2) < [x + (π/4)] < (π/2)

i.e. [(– 3π) / 4] < x < (π/4)

∴ f(x) is increasing when x ∈[– (π/2), (π/4)]

 i.e. f(x) will also be increasing in interval [0, (π/4)].