Question

The number of tangent(s) to the curve $y=\cos (x+y),-2\pi \le x\le 2\pi ,$ that is (are) perpendicular to the line $2x-y=3$ is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

$\frac{dy}{dx}=-\sin (x+y)(1+\frac{dy}{dx})$
Substituting $\frac{dy}{dx}=-\frac{1}{2}$ we get
$\sin (x+y)=1$
$\Rightarrow y=\cos (x+y)=0$
$\Rightarrow \sin x=1\Rightarrow x=\frac{\pi }{2},\frac{-3\pi }{2}$
No. of points $=2$