Question

Value of `sin(pi/3 - sin^1 (- 1/2))` is equal to

Options

• `1/2`

• `1/3`

• `1/4`

• 1

Answer 1

1

Explanation:

Let `sin - (- 1/2) = x ⇒ sin x`

= `- 1/2 = - sin  pi/6 = sin (- pi/6)`

Range of the principal value of `sin^-1 x` is

`[pi/2, pi/2] sin^-1 ((-1)/2) = pi/6`

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

= `sin((3pi)/6) = sin(pi/2)` = 1