tangents and normal

find all the tangents to the curve y = cos ( x+y ) ,-2piâ‰¤xâ‰¤2pithat are parallel to the line x + 2y = 0

1 Answers

the slope is -1/2

dy/dx=-sin(x+y)[1+dy/dx]

dy/dx = -sin(x+y)/[1+sin(x+y)]

equating it to -1/2,

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

sin (x+y) = 1

thus, cos (x+y)=0

so, y = 0

also sin (x+0)=1

Now you can proceed?

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