Question

`sin[pi/3 - sin^(-1) (-1/2)]` is equal to ______.

Options

• `1/2`

• `1/3`

• `1/4`

• 1

Answer 1

`sin[pi/3 - sin^(-1) (-1/2)]` is equal to 1.

Explanation:

`sin [pi/3 - sin^-1 (- 1/2)]`

⇒ `sin^-1 (-1/2)` = x

⇒ sin x = `-1/2`

= `- sin  pi/6 `

= `sin (- pi/6)`

∴ `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