Application of Derivatives 1 Question 21

21. Find all the tangents to the curve y=cos(x+y), 2πx2π, that are parallel to the line x+2y=0.

(1985,5M)

Integer Answer Type Question

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Solution:

  1. Given, y=cos(x+y)

dydx=sin(x+y)1+dydx

Since, tangent is parallel to x+2y=0,

then slope dydx=12

From Eq. (i), 12=sin(x+y)112

sin(x+y)=1, which shows cos(x+y)=0.

y=0

x+y=π2 or 3π2x=π2 or 3π2

Thus, required points are π2,0 and 3π2,0

Equation of tangents are

y0xπ/2=12

and

y0x+3π/2=122y=x+π2

and

2y=x3π2

x+2y=π2

and

x+2y=3π2

are the required equations of tangents.



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