give the range of sin-1x + cosec-1x

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Please find below the solution to the asked query:

We havefx=sin-1x+cosec-1xWe know thatsin-1x is defined for -1x1and cosec-1x is deined for x-1 and x1Hence only two values of x are common in domain sin-1x and cosec-1xwhich are -1 and 1. Hence domain of fx=sin-1x+cosec-1x is -1,1f1=sin-11+cosec-11=π2+π2=πf-1=sin-1-1+cosec-1-1=-π2-π2=-πHence range is -π,π

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Range for Sin-1 x = (-90,90)
Range for Cosec-1x=[-90,90]
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