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Question
The value of `sin^-1(cos (53pi)/5)` is ______
Options
`(-3pi)/5`
`(-pi)/10`
`(3pi)/5`
`pi/10`
MCQ
Fill in the Blanks
Solution
The value of `sin^-1(cos (53pi)/5)` is `underline((-pi)/10)`.
Explanation:
`cos (53pi)/5 = cos((50pi)/5 + (3pi)/5)`
= `cos(10pi + (3pi)/5)`
= `cos (3pi)/5`
= `sin (pi/2 - (3pi)/5) = sin((-pi)/10)`
∴ `sin^-1(cos (53pi)/5) = sin^-1(sin (-pi)/10) = (-pi)/10`
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