Question

$cot\left[{\cos }^{-1}\left(\frac{7}{25}\right)\right]=?$

• A. $\frac{25}{24}$
• B. $\frac{25}{7}$
• C. $\frac{24}{25}$
• D. None of these

Answer 1

The correct option is D

None of these

Explanation for the correct option:

Step 1. Find the value of given equation:

Let ${\cos }^{-1}\left(\frac{7}{25}\right)=A$

$\Rightarrow$ $\cos A=\frac{7}{25}$

Step 2. Use the identity $\mathit{s}\mathit{i}{\mathit{n}}^{\mathbf{2}}\mathit{A}\mathbf{}\mathbf{+}\mathbf{}\mathit{c}\mathit{o}{\mathit{s}}^{\mathbf{2}}\mathit{A}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}$,

$\Rightarrow$$\sin A=\sqrt{(1–{\cos }^{2}A)}$

$=\sqrt{1–\frac{49}{625}}$

$=\sqrt{\frac{576}{625}}$

$=\frac{24}{25}$

As we know,

$\mathit{c}\mathit{o}\mathit{t}\mathbf{}\mathit{A}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{}\mathbf{A}}{\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{}\mathbf{A}}$

$=\frac{\left({\displaystyle \frac{7}{25}}\right)}{\left({\displaystyle \frac{24}{25}}\right)}$

$=\frac{7}{24}$

$\therefore$$cot\left[{\cos }^{-1}\left(\frac{7}{25}\right)\right]=cotA$

$=\frac{\mathbf{7}}{\mathbf{24}}$

Hence, Option ‘D’ is Correct.