If $x\, cos (a+y)+cos\, a\, sin (a+y) =0, $ then $\frac{dy}{dx}$ is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $-\frac{cos^2(a+y)}{cos\, a}$
$x\cos (a+y)=-\cos a\sin (a+y)$
$x=-\cos a\frac{\sin(a+y)}{\cos(a+y)}$
differentiating wrt x
$\frac{dx}{dy}=-\cos a\frac{(\cos^2(a+y)+\sin^2(a+y))}{\cos^2(a+y)}$
$⇒\frac{dy}{dx}=-\frac{\cos^2(a+y)}{\cos a}$