Question

The value of the expression sin [cot^–1 (cos (tan^–11))] is ______.

Options

• 0

• 1

• `1/sqrt(3)`

• `sqrt(2/3)`

Answer 1

The value of the expression sin [cot^–1 (cos (tan^–11))] is `sqrt(2/3)`.

Explanation:

`sin[cot^-1 (cos  pi/4)] = sin[cot^-1  1/sqrt(2)]`

= `sin[sin^-1  sqrt(2/3)]`

= `sqrt(2/3)`