1.

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) `y=pi/4`(c) `y=pi/6`(d) `y=pi/4`A. `x=pi/6`B. `y=pi/4`C. `y=pi/6`D. `x=pi/4`

Answer» Correct Answer - C::D
`(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`


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