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If sin^2theta=x^2-3x+3 is meaningful, th...

If `sin^2theta=x^2-3x+3` is meaningful, then find the values of x.

Text Solution

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The correct Answer is:
[1, 2]
`sin^2 theta=x^2-3x+3`
Now, `sin^2theta in[0,1]`
`rArrx^2-3x+3 in[0,1]`
`rArr0lex^2-3x+3le1`
Now, `x^2-3x+3ge0` is always true. Thus,
`c^2-3x+3le1`
`or x^2-3x+2le0`
`or (x-1)(x-2)le0`
`or x in [1,2]`
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