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If `x tan 30^(@)+y cot 60^(@) =0 and 2x-y tan 45^(@)=1`, then calculate the values of x and y.

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Given that `x tan 30^(@)+y cot 60^(@)=0`
`or, x xx (1)/(sqrt(3)) +y xx (1)/(sqrt(3))=0 or, x+y=0 ["multiplying by " sqrt(3)] ……………..(1)`
Again, `2x-y tan45^(@) =1 " " or, 2x-y xx 1=1 " " or, 2x-y=1 ……..(2)`
Adding (1) and (2) we get, `3x=1 " " or, x=(1)/(3).`
`therefore `from (1) we get, `(1)/(3)+y=0 " " or, y=-(1)/(3).`
Hence the values of `x=(1)/(3) and y=-(1)/(3)`.

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