Question

If `x=sin^-1(sin10)` and `y=cos^(-1)(cos10)`, then the value of `(y-x)` is (a) `pi` (b) `7pi` (c) `0` (d) `10`

Answer 1

Correct Answer - D
The graph of `y = sin ^(-1) ( sin x ) `is

` therefore x = sin ^(-1) (sin 10) = - 10 + 3pi" " ` … (i)
and the graph of `y = cos ^(-1) ( cos x ) ` is

`therefore y = cos ^(-1) ( cos 10) = - 10 + 4 pi`
Now, from Eqs. (i) and (ii),
`y - x = (-10 + 4pi ) - (-10 + 3pi ) = pi`