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B
1,ifπ<x<2π
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C
1,if0<x<π
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D
−1,ifπ<x<2π
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Solution
The correct option is B1,ifπ<x<2π Wehave,sin−1(cosx)=π2−cos−1(cosx)=(π2−x,if0<x<ππ2−(2π−x),ifπ<x<2π=(π2−x,if0<x<πx−3π2,ifπ<x<2πClearly,itisnotdifferentiableatx=π.Therefore,ddx(sin−1(cosx)}=(−1,if0<x<π1,ifπ<x<2π