Question

The trigonometric equation $sin^{-1} x = 2\, sin^{-1}$ a, has a solution for

• A. $\frac{1}{2} < \left|a\right| < \frac{1}{\sqrt{2}}$
• B. all real values of a
• C. $\left|a\right| < \frac{1}{\sqrt{2}}$
• D. $\left|a\right| \le \frac{1}{\sqrt{2}}$

Answer 1

Answer: (D)

$\left|a\right| \le \frac{1}{\sqrt{2}}$

Answer 2

$-\frac{\pi}{4} \le \frac{sin^{2}\,x}{2} \le \frac{\pi}{4}$ $-\frac{\pi }{4} \le sin^{-1} \left(a\right) \le \frac{\pi}{4}$ $\frac{1}{2} \le \left|a\right| \le \frac{1}{\sqrt{2}}.$