Question

The value of the expression `2 sec^-1 2 + sin^-1 (1/2)` is ______.

Options

• `pi/6`

• `(5pi)/6`

• `(7pi)/6`

• 1

Answer 1

The value of the expression `2 sec^-1 2 + sin^-1 (1/2)` is `(5pi)/6`.

Explanation:

`2 sec^-1 2 + sin^-1  1/2 = 2sec^-1 (sec  pi/3) + sin^-1 (sin  pi/6)`

= `2 * pi/3 + pi/6`

= `(2pi)/3 + pi/6`

= `(5pi)/6`