#### Question

Write the interval in which f(x) = sin x + cos x, x ∈ [0, π/2] is increasing ?

#### Solution

\[f\left( x \right) = \sin x + \cos x, x \in \left[ 0, \frac{\pi}{2} \right]\]

\[f'\left( x \right) = \cos x - \sin x\]

\[\text { For f(x) to be increasing, we must have}\]

\[f'\left( x \right) > 0\]

\[ \Rightarrow \cos x - \sin x > 0\]

\[ \Rightarrow \sin x < \cos x\]

\[ \Rightarrow \frac{\sin x}{\cos x} < 1\]

\[ \Rightarrow \tan x < 1\]

\[ \Rightarrow x \in [0, \frac{\pi}{4}]\]

Is there an error in this question or solution?

Solution Write the Interval in Which F(X) = Sin X + Cos X, X ∈ [0, π/2] is Increasing ? Concept: Increasing and Decreasing Functions.