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NDA 2025 Maths · Mathematics · Application of Derivatives · easy

F(x)=sin x is increasing in the interval (0,(π)/(2)). 2. f(x)=cos x is increasing in the interval (0,(π)/(2)).

Single correct option

Consider the following statements:
1. f(x)=sin⁡xf(x)=\sin x is increasing in the interval (0,π2)\left(0,\dfrac\pi2\right).
2. f(x)=cos⁡xf(x)=\cos x is increasing in the interval (0,π2)\left(0,\dfrac\pi2\right).
Which of the statements given above is/are correct?
  1. A. 11 only
  2. B. 22 only
  3. C. Both 11 and 22
  4. D. Neither 11 nor 22
Show answer and solution

Answer: (A) 11 only

f′(x)=cos⁡x>0f'(x)=\cos x>0 on (0,π2)\left(0,\frac\pi2\right), so sin⁡x\sin x is increasing: statement 1 is correct. For cosine, f′(x)=−sin⁡x<0f'(x)=-\sin x<0 on the same interval, so it is decreasing (from 11 to 00): statement 2 is false.
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Original question written in the NDA 2025 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake