Question

refer to the attachment for the question..


class 11..math​

Answer 1

Step-by-step explanation:

range of sin x= 0 to 1

range of cos x= 1 to 0

so if we subtract cos x from sin x we will get values ranging from 0 to 1

they might be in negative also, but since mod is used they will be positive.

hence maximum value of the equation is 1

Answer 2

Solution :

$\sf \bigg | \bigg( \sin \: x \: - \cos \: x \bigg)\bigg | \\ \\ \\ \ \implies \sf \bigg | \sqrt{2} \bigg( \cos \frac{ \pi}{4} \: \sin \: x - \cos \: x \: \sin \frac{ \pi}{4} \bigg) \bigg | \\ \\ \\ \implies \sf\bigg | \sqrt{2} \: \sin ( x - \frac{ \pi}{4}) \bigg | \\ \\ \\ \sf \checkmark \: \: minimum \: \: value \: \: of \: \: sin \theta \: \: is \: - 1 \: \& \: \: maximum \: \: value \: \: is \: \: 1 \\ \\ \\ \begin{array}{c |c} \implies \sf \bigg | \sqrt{2} \times ( - 1) \bigg| \: \: \: \: \: \: \: \: & \implies \sf \: \bigg | \sqrt{2} \times (1) \bigg | \end{array} \\ \\ \large { \therefore \: \: \tt\color{pink}{ maximum \: \: value \: \: of \: \: the \: \: function \: \: is \: \: \sqrt{2} }}$

[note : always try to express into same trigonometric ratios for this kind of questions]

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Let's understand Graph of the function

→ Modulus of a function f ( x ) means it's not derivable on the x axis. Or we can say it changes the slope on the x axis. And it's always on the 1st and 2nd coordinate.

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