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Find the equation of tangents to the cur...

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

Text Solution

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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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