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Question

In a triangle ABC, if cotA=(x3+x2+x)1/2,cotB=(x+x1+1)1/2 and cotC=(x3+x2+x1)1/2, then the triangle is

A
isosceles
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B
obtuse angled
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C
right angled
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D
equilateral
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Solution

The correct option is B right angled
Given, cotA=(x3+x2+x)12.
And
cotC=(x3+x2+x1)12
Hence
tanC=(x3+x2+x1)12

=1+x+x2xx

=xcotBxx
xtanC=cotB
cotC.cotB=x
If x=1
We get, cotCcotB=1
Then
B=π2C
Hence a right angled triangle.

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