Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which satisfy ${\sin ^{ - 1}}\left( {{{3x} \over 5}} \right) + {\sin ^{ - 1}}\left( {{{4x} \over 5}} \right) = {\sin ^{ - 1}}x$ is equal to :

Question

Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which satisfy

${\sin ^{ - 1}}\left( {{{3x} \over 5}} \right) + {\sin ^{ - 1}}\left( {{{4x} \over 5}} \right) = {\sin ^{ - 1}}x$ is equal to :

Solution

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