Question

If sin `(sin^-1  1/3 + cos^-1 x) = 1`, then the value of x is ______.

Options

• `1/2`

• `1/3`

• `1/4`

• `1/6`

Answer 1

If sin `(sin^-1  1/3 + cos^-1 x) = 1`, then the value of x is `underline(1/3)`.

Explanation:

sin `(sin^-1  1/3 + cos^-1 x) = 1`

`=> sin (sin^-1  1/3 + cos^-1  x) = sin  pi/2`

`=> sin^-1  1/3 = pi/2 - cos^-1 x`

`=> sin^-1  1/3 = sin^-1 x   ...[because sin^-1 x + cos^-1 x = pi/2]`

`=> x = 1/3`