1.

The solution of the system of equations `sinxsiny=(sqrt(3))/4,cosxcosy=(sqrt(3))/4`are`x_1=pi/3+pi/2(2n+k); n , k in I``y_1=pi/6+pi/2(k-2n); n , k in I``x_2=pi/6+pi/2(2n+k); n , k in I``y_2=pi/3+pi/2(k-2n); n , k in I`

Answer» `sinx*siny=sqrt3/4`
`cosx*cosy+sinxsiny=sqrt3/2`
`cos(x-y)=sqrt3/2`
`x-y=2npipmpi/6`
`cosxcosy=sqrt3/4`
`cosxcosy-sinxsiny=0`
`cos(x+y)=0`
`x+y=(2n+1)pi/2`
`x+y=npi+pi/2`
`2x=2npipmpi/6+npi+pi/2`
`x=(2n+1)pi/2+pi/4pmpi/2`
`2y=4pi+pi/2-2npipmpi/6`
`y=(1-2n)pi+pi/4pmpi/2`.


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