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Question

x+y=1,xy=2, then tan-1x+tan-1y=


A

π4

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B

3π4

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C

3π2

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D

π2

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Solution

The correct option is B

3π4


Explanation for the correct option:

Calculate the value of the expression tan-1x+tan-1y

It is given that,

x+y=1 and xy=2

We know that, if x>0,y>0 and xy>1 then

tan-1x+tan-1y=π+tan-1x+y1-xy

tan-1x+tan-1y=π+tan-111-2

tan-1x+tan-1y=π+tan-1-1

tan-1x+tan-1y=π+-π4 tan-1-1=-π4

tan-1x+tan-1y=4π-π4

tan-1x+tan-1y=3π4

Hence, the correct option is B)3π4.


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