Share

Books Shortlist

# Solution for Show that F(X) = Cos X is a Decreasing Function on (0, π), Increasing in (−π, 0) and Neither Increasing Nor Decreasing in (−π, π) ? - CBSE (Commerce) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

#### Question

Show that f(x) = cos x is a decreasing function on (0, π), increasing in (−π, 0) and neither increasing nor decreasing in (−π, π) ?

#### Solution

$\text { Here },$

$f\left( x \right) = \cos x$

$\text { Domain of cos x is }\left( - \pi, \pi \right).$

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

$\text { For } x \in \left( - \pi, 0 \right), \sin x < 0 \left[ \because \text { sine function is negative in third and fourth quadrant } \right]$

$\Rightarrow - \sin x > 0$

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

$\text { So, cos x is increasing in} \left( - \pi, 0 \right) .$

$\text { For x } \in \left( 0, \pi \right)),\sin x > 0 \left[ \because sine \text { function is positive in first and second quadrant } \right]$

$\Rightarrow - \sin x < 0$

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

$\text { So,f(x) is decreasing on }\left( 0, \pi \right).$

$\text { Thus,f(x) is neither increasing nor decreasing in }\left( - \pi, \pi \right).$

Is there an error in this question or solution?

#### Video TutorialsVIEW ALL [3]

Solution Show that F(X) = Cos X is a Decreasing Function on (0, π), Increasing in (−π, 0) and Neither Increasing Nor Decreasing in (−π, π) ? Concept: Increasing and Decreasing Functions.
S