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  • Need solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Fill in the blanks question 15

Need solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Fill in the blanks question  15

Answers (1)

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Answer: f^{1}\left(\frac{\pi}{6}\right)=\frac{1+\sqrt{3}}{2}

Hint:

Given: f(x)=|\sin x-\cos x|

Solution:  f(x)=|\sin x-\cos x|

\begin{aligned} &f(x)=\left(\begin{array}{cc} \sin x-\cos x & 0 \leq x \leq \frac{\pi}{4} \\\\ -(\sin x-\cos x) & \frac{\pi}{4}<x \leq \frac{\pi}{4} \end{array}\right) \\\\ &f^{{}'}(x)=\left(\begin{array}{cc} \sin x+\cos x & 0 \leq x \leq \frac{\pi}{4} \\\\ -(\sin x+\cos x) & \frac{\pi}{4}<x \leq \frac{\pi}{4} \end{array}\right) \end{aligned}

\begin{aligned} f^{{}'}\left(\frac{\pi}{6}\right)=& \sin \frac{\pi}{6}+\cos \frac{\pi}{6} \\\\ &=\frac{1}{2}+\frac{\sqrt{3}}{2} \\\\ \end{aligned}

                    =\frac{\sqrt{3}+1}{2}

 

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