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Question
The value of `sin^-1 (cos((43pi)/5))` is ______.
Options
`(3pi)/5`
`(-7pi)/5`
`pi/10`
`- pi/10`
Solution
The value of `sin^-1 (cos((43pi)/5))` is `- pi/10`.
Explanation:
`sin^-1 (cos (40pi + 3pi)/5) = sin^-1 cos(8pi + (3pi)/5)`
= `sin^-1 (cos (3pi)/5)`
= `sin^-1 (sin(pi/2 - (3pi)/5))`
= `sin^-1 (sin(- pi/10))`
= `- pi/10`.
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