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Draw the graph of y=sin(sin^(-1)x) or y=...

Draw the graph of `y=sin(sin^(-1)x)` or `y=cos(cos^(-1)x)`

Text Solution

Verified by Experts

`y = sin(sin^(-1)y)`
Clearly, the domain of the function is [-1,1].
`"Now "-1le x le 1`
`therefore" "pi/2lesin^(-1)xlepi/2`
`therefore" "-1lesin(sin^(-1)x)le1`
`"Also "f(x) = sin (sin^(-1)x)=x, "for "x in [-1, 1]`
`y=cos (cos^(-1)x)`
Clearly the domin of the function is [-1, 1].
`"Now "-1lexle1`
`therefore" "0lecos^(-1)xlepi`
`therefore" "-1lecon(cos^(-1)x)le1`
Also `f(x) =cos (cos^(-1)x)=x, for x in [-1, 1]`
Thus, the grah of both the functions is `t=x for `x in [-1, 1]`
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