Question: If sin{sin^-1 (1/5) + cos^-1 x} = 1 then find the value of x

Solution:

Given, sin{sin^-1 (1/5) + cos^-1 x} = 1

=> sin^-1 (1/5) + cos^-1 x = sin^-1 1       {since sin(π/2) = 1}    

=> sin^-1 (1/5) + cos^-1 x = π/2

=> sin^-1 (1/5) = π/2 - cos^-1 x     

=> sin^-1 (1/5) = sin^-1 x               {since sin^-1 x + cos^-1 x = π/2}

=> x = 1/5

So, the value of x is 1/5