Q. 325.0( 1 Vote )

Find the equation

Answer :

y = cos(x + y)


we have to find equation of tangent which is parallel to x + 2y = 0


Slopes of parallel lines are equal hence slope of line x + 2y = 0 will be the slope of tangent


Let us find slope of line by writing it in form y = mx + c


x + 2y = 0


2y = -x


y = -(1/2)x


Hence slope of line is -(1/2) and hence slope of tangent is -(1/2)


Slope of tangent is given by hence


Now to find equation of tangent we need point on curve where the slope is -(1/2)


Differentiate given y with respect to x







Put slope



1 + sin(x + y) = 2sin(x + y)


sin(x + y) = 1


Hence x + y = 90°


Put this value of (x + y) in curve equation y = cos(x + y)


y = cos90°


y = 0


Put y = 0 in sin(x + y) = 1


sinx = 1


Now given that x is from -2π to 2π hence we get sinx = 1 for two values of x


One is and other is


Hence we have two points on curve where slope of tangent is -(1/2)


Those points are and and hence we have 2 tangents


Writing equation of those tangents using slope point form


Tangent passing through and having slope -1/2




4y = -2x + π


2x + 4y = π


Tangent passing through and having slope -1/2




4y = -2x – 3π


2x + 4y = -3π


Hence equations of tangents to curve y = cos(x + y) that are parallel to the line x + 2y = 0 are 2x + 4y = π and 2x + 4y = -3π

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