If `xa n dy` are positive acute angles such that `(x+y)` and `(x-y)` satisfy the equation `tan^2theta-4tantheta+1=0,` then `x=pi/6` (b) `x=pi/4` (c) `y=pi/6` (d) `y=pi/4`

Options

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

Answer

C, D

Explanation

`(x+y)` and `(x-y)` satisfy the equation `tan^(2) theta-4 tan theta+1=0`. Thus,
`tan (x+y)+tan (x-y)=4`
and `tan (x+y)tan (x-y)=1`
`:. Tan2x=tan ((x+y)+(x-y))`
or `tan 2x= (tan (x+y)+tan (x-y))/(1-tan (x+y) tan (x-y))`
`:. Tan2x=oo`
or `2x=90^(@)`
or `x=45^(@)=pi/4`
`:. y=pi/6`