Applications Of Derivatives Question 17
Question: The equation of one of the tangents to the curve $ y=\cos (x+y),-2\pi \le x\le 2\pi $ that is parallel to the line $ x+2y=0, $ is
Options:
A) $ x+2y=1 $
B) $ x+2y=\pi /2 $
C) $ x+2y=\pi /4 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ y=\cos (x+y)….(1) $
$ \therefore \frac{dy}{dx}=-\sin (x+y){ 1+\frac{dy}{dx} } $
$ =-\frac{\sin (x+y)}{1+\sin (x+y)}=-\frac{1}{2} $
$ \Rightarrow \sin (x+y)=1, $ so $ \cos (x+y)=0 $
$ \therefore $ from $ (1)y=0 $ and $ (x+y)=2n\pi +\frac{\pi }{2} $ Tangent at $ ( \frac{\pi }{2},0 ) $ is $ x+2y=\frac{\pi }{2} $
BETA
