Question

If ${\sin }^{-1}\left(\frac{x}{13}\right)+cose{c}^{-1}\left(\frac{13}{12}\right)=\frac{\pi }{2}$ , then the value of x is

• A. 5
• B. 4
• C. 12
• D. 11

Answer 1

Answer: (A)

$si{n}^{-1}\left(\frac{x}{13}\right)=\frac{\pi }{2}-cose{c}^{-1}\left(\frac{13}{12}\right)$
[From given equation]
$=se{c}^{-1}\left(\frac{13}{12}\right)=co{s}^{-1}\left(\frac{12}{13}\right)=si{n}^{-1}\frac{5}{13}$
$\therefore \frac{x}{13}=\frac{5}{13}$
$\Rightarrow x=5$