Find the equation of tangents to the curve `y=cos(x+y),-2pilt=xlt=2pi` that are parallel to the line `x+2y=0.`

Explanation

Equation of the line parallel to the tangent is,

`x+2y = 0 => y = -1/2x`

`:.` Slope`(m) = -1/2`

So, slope of the tangent will be `-1/2`.

Now, `y = cos(x+y)`

`=>dy/dx = -sin(x+y)(1+dy/dx)`

As `m = -1/2, :. dy/dx = -1/2`

`=> -1/2 = -sin(x+y)(1-1/2)`

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