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# Solution for Write the Interval in Which F(X) = Sin X + Cos X, X ∈ [0, π/2] is Increasing ? - CBSE (Science) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

#### Question

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

#### Solution

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

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

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

$f'\left( x \right) > 0$

$\Rightarrow \cos x - \sin x > 0$

$\Rightarrow \sin x < \cos x$

$\Rightarrow \frac{\sin x}{\cos x} < 1$

$\Rightarrow \tan x < 1$

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

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