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Question

The number of solutions of the equation sin1(1+x22x)=π2sec(x1) is

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Solution

Since, domain of sin1x is [1,1]
Therefore, 11+x22x1
1+2x+x20 and 12x+x20
(1+x)20 and (1x)20
1x1
However, only x=1 satisfies the above equation.
Therefore, only one solution exists.

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