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Question

If x+1x=2, then the principal value of sin-1x is


A

π4

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B

π2

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C

π

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D

3π2

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Solution

The correct option is B

π2


Explanation for the correct option.

Step 1. Solve the equation for x.

The given equation x+1x=2 can be solved for x as:

x+1x=2x2+1=2xx2-2x+1=0x-12=0x-1=0x=1

Step 2. Find the value of sin-1x.

As the value of x for the given equation is 1. So in the expression sin-1x substitute 1 for x and find its value.

sin-1x=sin-11=π2sinπ2=1

So for the equation x+1x=2, the principal value of sin-1x is π2.

Hence, the correct option is B.


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