PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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# Solution for Find the Intervals in Which F(X) = Sin X − Cos X, Where 0 < X < 2π is Increasing Or Decreasing ? - PUC Karnataka Science Class 12 - Mathematics

#### Question

Find the intervals in which f(x) = sin x − cos x, where 0 < x < 2π is increasing or decreasing ?

#### Solution

$f\left( x \right) = \sin x - \cos x, x \in \left( 0, 2\pi \right)$

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

$\text { Forf(x) to be increasin, we must have }$

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

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

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

$\Rightarrow \tan x > - 1$

$\Rightarrow x \in \left( 0, \frac{3\pi}{4} \right) \cup \left( \frac{7\pi}{4}, 2\pi \right)$

$\text { So,f(x)is increasing on } \left( 0, \frac{3\pi}{4} \right) \cup \left( \frac{7\pi}{4}, 2\pi \right) .$

$\text { Forf(x) to be decreasing we must have},$

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

$\Rightarrow \cos x + \sin x < 0$

$\Rightarrow \sin x < - \cos x$

$\Rightarrow \tan x < - 1$

$\Rightarrow x \in \left( \frac{3\pi}{4}, \frac{7\pi}{4} \right)$

$\text { So,f(x)is decreasing on }\left( \frac{3\pi}{4}, \frac{7\pi}{4} \right).$

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Solution Find the Intervals in Which F(X) = Sin X − Cos X, Where 0 < X < 2π is Increasing Or Decreasing ? Concept: Increasing and Decreasing Functions.
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