If `xa n dy` are positive acute angles such that `(x+y)` and `(x-y)` satisfy the equation `tan^2theta-4tantheta+1=0,` then

Options

A. `x=pi/6`
B. `y=pi/4`
C. `y=pi/6`
D. `y=pi/4`

Explanation

`tan^2theta-4tantheta+1=0`

Sum of roots=`-b/a=4`

Product of roots=`c/a=1`

`tan(x+y)+tan(x-y)=4`

`tan2x=tan[(x+y)+(x-y)]`

`=(-tan(x+y)+tan(x-y))/(1-tanxtany)`

`=4/(1-1)=oo`

`tan2x=oo`

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