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In a right triangle AB C, right angled a...

In a right triangle `AB C`, right angled at `B ,`the ratio of `AB : AC`is `1:sqrt(2)`. Find the value of`(2tanA)/(1+tan^2A)`

A

`1/4`

B

`1/2`

C

`4`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
D
Consider a`Delta ABC"in which "angle B=90^(@)and AB:AC=1:sqrt(2).`
Let `AB=x,Then ,AC=sqrt(2)x.`
By pythagoras' theorem , we have
`AC^(2)=AB^(2)+BC^(2)implies BC^(2)=AC^(2)-AB^(2)`
`implies BC^(2) =(sqrt(2)x)^(2)-(x)^(2)2x^(2)-x^(2) =x^(2)`
`implies BC=x.`
`therefore tan A=(BC)/(AB)=(x)/(x)=1.`
SO , the given expression `=((2tan A)/(1+ tan ^(2)A))=((2xx1)/(1+1))=(2)/(2)=1.`
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