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NDA 2016 Maths · Mathematics · Inverse Trigonometric Functions · easy

Cos ^-1(-x)=-cos ^-1x for x∈[-1,1]. 2. sin ^-1x+cos ^-1x=(π)/(2) for x∈[-1,1].

Single correct option

Consider the following statements:
1. cos⁡−1(−x)=−cos⁡−1x\cos^{-1}(-x)=-\cos^{-1}x for x∈[−1,1]x\in[-1,1].
2. sin⁡−1x+cos⁡−1x=π2\sin^{-1}x+\cos^{-1}x=\dfrac\pi2 for x∈[−1,1]x\in[-1,1].
Which of the statements given above is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (B) 2 only

The correct identity is cos⁡−1(−x)=π−cos⁡−1x\cos^{-1}(-x)=\pi-\cos^{-1}x; the statement would make the value negative, which lies outside the range [0,π][0,\pi], so statement 1 is false. Statement 2 is the standard complementary identity and holds on the whole interval [−1,1][-1,1].
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Original question written in the NDA 2016 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