If $$sin\frac{\pi{x}}{2}=x^{2}-2x+2$$, then the value of x is
$$sin\frac{\pi{x}}{2}=x^{2}-2x+2$$
We know that sin can take only 3 integral values, 1,0, and -1.
$$x^{2}-2x+2$$ cannot be equal to -2. Any negative value of x will increase the value of expression beyond 4.
The value of the expression can be made equal to 1 (By substituting x = 1).
X = 1 also satisfies the LHS as sin 90 = 1.
Hence, option B is the right answer.
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