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The value of $\cot\bigg(\cos^{-1}\frac{7}{25}\bigg)$ is

\[(A)\quad\frac{25}{24}\quad(B)\quad\frac{25}{7}\quad(C)\quad\frac{24}{25}\quad(D)\quad\frac{7}{24}\]

1 Answer

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  • \(cos\theta=x\:\Rightarrow\:cot\theta=\large\frac{x}{\sqrt{1-x^2}}\)
Ans - (D)
Put \( cos^{-1}\frac{7}{25}=\theta\)
\( \Rightarrow cos\theta=\large\frac{7}{25}\)
\(\Rightarrow\:cot(cos^{-1}\large\frac{7}{25})\) = cot\(\theta\)
 
By taking \(x=\frac{7}{25}\),from the above formula of cot\(\theta\), we get
\( \Rightarrow cot\theta=\large\frac{\frac{7}{25}}{\sqrt{1-\large\frac{49}{625}}}=\frac{7}{25}.\large\frac{25}{24}=\large\frac{7}{24}\)\
\(\Rightarrow\:cot(cos^{-1}\large\frac{7}{25}) = \large\frac{7}{24}\)

 

answered Feb 18, 2013 by thanvigandhi_1
edited Mar 16, 2013 by thanvigandhi_1
 

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