Question

If x > 0 and sin^–1$\left( \frac{5}{x} \right)$+ sin^–1$\left( \frac{12}{x} \right)$= $\frac{\pi}{2}$ then x =

• A. 7
• B. 13
• C. 17
• D. 34

Answer 1

Answer: (B)

13

Answer 2

sin^–1$\frac{5}{x}$ + sin^–1$\frac{12}{x}$ = $\frac{\pi}{2}$

sin^–1$\frac{5}{x}$=$\frac{\pi}{2}$ – sin^–1$\frac{12}{x}$

$\frac{5}{x}$ = sin$\left( \frac{\pi}{2}–\sin^{–1}\frac{12}{x} \right)$

̃$\frac{5}{x}$=cos sin^–1$\frac{5}{x}$=$\frac{\sqrt{x^{2}–144}}{x}$, x ¹ 0 25 = x² –144

̃ x² = 169 ̃ x = 13