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Question

If a is any real number,the number of roots of cot x =a in the first quadrant is (are).

 



A

2

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B

0

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C

1

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D

none of these

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Solution

The correct option is B

1


Given:cot xtan x=a1tan xtan x=a1tan2x=a tan xtan2 x+a tan x1=0It is a quadratic equation.If tan x=z,then the equation becomesz2+az1=0z=a±a2+42tan x=a±a2+42x=tan1(a±a2+42)There are two roots of the given equation,but we need to find the number of roots in the first quadrant.that is exactly one root of the equation,that is ,x=tan1 (a±a2+42)


Mathematics
RD Sharma
Standard XI

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