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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2023 · Mathematics · Inverse Trigonometric Functions

If ^ -1 p-cosec^ -1 q=0 , where p > 0, q > 0 ; then what is the...

If sec⁡−1p−cosec⁡−1q=0\sec ^{-1} p-\operatorname{cosec}^{-1} q=0, where p>0,q>0\mathrm{p} > 0, \mathrm{q} > 0; then what is the value of \mathrmp−2+\mathrmq−2\mathrmp^{-2}+\mathrmq^{-2} ?

Options

  1. A1
  2. B2
  3. C12\frac{1}{2}
  4. D122\frac{1}{2 \sqrt{2}}

Correct answer

A. 1

Step-by-step solution

 Given, sec⁡−1p−cosec⁡−1q=0⇒cos⁡−1(1p)=sin⁡−1(1q)⇒(1p)2+(1q)2=1⇒p−2+q−2=1\begin{aligned} & \text{ Given, } \sec ^{-1} \mathrm{p}-\operatorname{cosec}^{-1} \mathrm{q}=0 \\ & \Rightarrow \cos ^{-1}\left(\frac{1}{\mathrm{p}}\right)=\sin ^{-1}\left(\frac{1}{\mathrm{q}}\right) \\ & \Rightarrow\left(\frac{1}{\mathrm{p}}\right)^2+\left(\frac{1}{\mathrm{q}}\right)^2=1 \\ & \Rightarrow \mathrm{p}^{-2}+\mathrm{q}^{-2}=1\end{aligned}
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