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Question
`sin[pi/3 - sin^(-1) (-1/2)]` is equal to ______.
Options
`1/2`
`1/3`
`1/4`
1
Solution
`sin[pi/3 - sin^(-1) (-1/2)]` is equal to 1.
Explanation:
`"sin" [pi/3 - "sin"^-1 (- 1/2)]`
`Rightarrow "sin"^-1 (-1/2) = x`
`Rightarrow "sin x" = -1/2 `
`= - "sin" pi/6 `
`= sin (- pi/6)`
`Rightarrow therefore "sin"^-1 (-1/2)`
` = - pi/6`
`Rightarrow therefore "sin" [pi/3 - "sin"^-1 (-1/2)]`
`= "sin" (pi/3 + pi/6)`
`= "sin" ((3pi)/6)`
`= "sin" (pi/2)`
= 1
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