Question

If sin `("sin"^-1 1/5 + "cos"^-1 "x") = 1,` then the value of x is ____________.

Options

• -1

• `2/5`

• `1/3`

• `1/5`

Answer 1

If sin `("sin"^-1 1/5 + "cos"^-1 "x") = 1,` then the value of x is `bbunderline(1/5)`.

Explanation:

We have, sin `("sin"^-1 1/5 + "cos"^-1 "x") = 1,`

⇒ `"sin"^-1 1/5 + "cos"^-1 "x" = sin^(−1)(1)`

⇒ `"sin"^-1 1/5 + π/2 − sin^-1 x = π/2`

⇒ `"sin"^-1 1/5 − sin^(−1) x = 0`

⇒ `"sin"^-1 1/5 − sin^(−1) x ⇒ x  = sin(sin^(−1)  1/5)`

⇒ x = `1/5`