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Please solve RD Sharma class 12 chapter 16 Increasing and Decreasing Function Excercise Fill in the blanks Question 5: Maths Textbook Solution.

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Answer: The set of values of x for which f(x) is increasing are R=\left \{ (2n-1)\frac{\pi }{2},n\epsilon \mathbb{Z} \right \}

Hint: If f(x) is increasing then f'(x)>0

Given: f(x)=tanx-x

Explanation: It is given that,

f(x)=tanx-x                                                         …(i)

Differentiate (i)  with respect to x


So, sec^{2}x-1>0                          [  \because f(x) is increasing]

\Rightarrow sec^{2}x>1                    \forall x\epsilon R=\left \{ (2n-1)\frac{\pi }{2},n\epsilon \mathbb{Z} \right \}

Thus, the given function is increasing on R=\left \{ (2n-1)\frac{\pi }{2},n\epsilon \mathbb{Z} \right \}

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