Question

$x=sin\theta +\theta cos\theta ,y=cos\theta -\theta sin\theta ,then{\left(\frac{dy}{dx}\right)}_{\theta =\frac{\pi }{2}}$

• A. -π/2
• B. 2/π
• C. π/4
• D. 4/π

Answer 1

The correct option is D

4/π

$x=sin\theta +\theta cos\theta \Rightarrow \frac{dx}{d\theta }=2cos\theta -\theta sin\theta y=cos\theta +\theta sin\theta \Rightarrow \frac{dy}{d\theta }=-2sin\theta -\theta cos\theta \therefore \frac{dy}{dx}=\frac{-2sin\theta -\theta cos\theta }{2cos\theta -\theta sin\theta }$