Mathematics

The values of $$x$$ for the given equation $${\sec ^{ - 1}}\left( x \right) - {\sec ^{ - 1}}\left( {\sqrt 2 } \right) = \frac{\pi }{2}$$ is


ANSWER

$$-\sqrt{2}$$


SOLUTION
Consider the given equation.
$$\begin{array}{l} { \sec ^{ -1 }  }\left( x \right) -{ \sec ^{ -1 }  }\left( { \sqrt { 2 }  } \right) =\dfrac { \pi  }{ 2 }  \\ { \sec ^{ -1 }  }\left( x \right) =\dfrac { \pi  }{ 2 } +\dfrac { \pi  }{ 4 }  \\ { \sec ^{ -1 }  }\left( x \right) =\dfrac { { 3\pi  } }{ 4 }  \\ x=-\sqrt { 2 }  \\ Hence,\, option\, A\, is\, \, the\, \, correct\, answer.\,  \end{array}$$
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