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Draw the graph of y="cosec"("cosec"^(-1)...

Draw the graph of `y="cosec"("cosec"^(-1)x)" or "y=sec(sec^(-1)x)`.

Text Solution

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`y=cosec(cosec^(-1)x)`
Clearly, the domain of the function is `(-oo,-1]cup[1,oo)`.
Now `cosec^(-1)x in[-pi/2,0)cup(0,pi/2]`
`:." cosec"("cosec"^(-1)x)in(-oo,-1]cup[1,oo)`
Also f(x) `="cosec"("cosec"^(-1)x)=x, " for "x in (-oo, -1]cup[1,oo)`
`y=sec(cec^(-1)x)`
Clearly, the domain of the function is `(-oo,-1]cup[1,oo)`
Now `sec^(-1)x in[0,pi/2)cup(pi/2,pi]`
`:." "sec(sec^(-1)x)in (-oo, -1]cup[-1,oo)`.
Also `f(x)=sec(sec^(-1)x)x," for "x in (-oo, -1]cup[1,oo).`
Thus, the graph of both the functions is the straight line y = x for `x in (-oo, -1]cup [1,oo)`.
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