Question

 

If `sin (sin^(−1)  1/5+cos^(−1) x)=1`, then find the value of x.

 

Answer 1

Given:

`sin (sin^-1  1/5 + cos^-1 x) 1`

`=> sin^-1 (1/5) + cos^-1 x = sin^-1 1`

`=> sin^-1 (1/5) + cos^-1(x) pi/2`

`=> sin^-1 (1/5) = -cos^-1 x`

`=> sin^-1 (1/5) = sin^-1 x`

`(sin^-1x + cos^-1 x = pi/2)`

`x = 1/5`