Number of possible tangents to the curve y = c o s ( x + y ) , − 3 π ≤ x ≤ 3 π that are parallel to the line x+2y = 0, is Options: A . &nbsp 1 B . &nbsp 2 C . &nbsp 3 D . &nbsp 4

Answer: Option C : C We have, y = cos (x + y) d y d x = s i n ( x + y ) ( 1 + d y d x ) Since, the tangents are parallel to the line x + 2y = 0 − 1 2 = − s i n ( x + y ) ( 1 − 1 2 ) ⇒ s i n ( x + y ) = 1 ⇒ x + y = π 2 , 5 π 2 , 3 π 2 − 1 ≤ y ≤ 1. Hence (c) is the correct answer.

Number of possible tangents to the curve y=cos(x+y),−3π≤x&

Discussion Forum : Application Of Derivatives

Question -

Number of possible tangents to the curve $y = c o s (x + y), - 3 π \leq x \leq 3 π$ that are parallel to the line x+2y = 0, is

Options:

A . 1

B . 2

C . 3

D . 4

Answer: Option C
:
C

We have, y = cos (x + y)
$\frac{d y}{d x} = s i n (x + y) (1 + \frac{d y}{d x})$
Since, the tangents are parallel to the line x + 2y = 0
$- \frac{1}{2} = - s i n (x + y) (1 - \frac{1}{2}) \Rightarrow s i n (x + y) = 1 \Rightarrow x + y = \frac{π}{2}, \frac{5 π}{2}, \frac{3 π}{2} - 1 \leq y \leq 1.$
Hence (c) is the correct answer.

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