Question

Number of possible tangents to the curve $y=cos(x+y),-3\pi \le x\le 3\pi$ that are parallel to the line x+2y = 0, is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C

3

We have, y = cos (x + y)
$\frac{dy}{dx}=sin(x+y)(1+\frac{dy}{dx})$
Since, the tangents are parallel to the line x + 2y = 0
$-\frac{1}{2}=-sin(x+y)(1-\frac{1}{2})\Rightarrow sin(x+y)=1\Rightarrow x+y=\frac{\pi }{2},\frac{5\pi }{2},\frac{3\pi }{2}-1\le y\le 1.$
Hence (c) is the correct answer.