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Question
`sin[pi/3 - sin^(-1) (-1/2)]` is equal to ______.
Options
`1/2`
`1/3`
`1/4`
1
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Solution
`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
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