Consider the equation sin−1x2−6x+172+cos−1k=π2 then

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The largest value of k for which the equation has 2 distinct solutions is 1

The eqution must have real roots if k∈-12,1

the equation must have real roots if k∈-1,12

The equation has unique solution if k=-12

answer is A.

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Detailed Solution

sin−1x2−6x+172=sin−1kThe above equation has solutions only when -1≤k≤1The graph of the curve y=x2-6x+172 is as below

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