The trigonometric equation ${\sin ^{ - 1}}x = 2{\sin ^{ - 1}}a$ has a solution for :
$\left| a \right| \ge {1 \over {\sqrt 2 }}$
${1 \over 2} < \left| a \right| < {1 \over {\sqrt 2 }}$
all real values of $a$
$\left| a \right| \le {1 \over {\sqrt 2 }}$
