Question

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

• A. 5
• B. 4
• C. 12
• D. 11

Answer 1

Answer: (A)

5

Answer 2

$sin^{-1}\left(\frac{x}{13}\right) = \frac{\pi}{2}-cosec^{-1}\left(\frac{13}{12}\right)$ $\quad$[From given equation] $= sec^{-1}\left(\frac{13}{12}\right) = cos^{-1}\left(\frac{12}{13}\right) = sin^{-1} \frac{5}{13}$ $\therefore \frac{x}{13} = \frac{5}{13}$ $\Rightarrow x= 5$