Question

If $y=1$$-$$\cos \theta$ & $x=1$$-$$\sin \theta$ then, $\frac{dy}{dx}$ at $\theta$$=$$\frac{\pi }{4}$ is,

• A. $-1$
• B. $1$
• C. $\frac{1}{2}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

The correct option is A $-1$

Given

$y=1-\cos \theta$

$\frac{dy}{d\theta }=-(-\sin \theta )$

$\frac{dy}{d\theta }=\sin \theta \cdots \left(1\right)$

$x=1-\sin \theta$

$\frac{dx}{d\theta }=-\cos \theta \cdots \left(2\right)$

From $\left(1\right)$ and $\left(2\right)$

$⟹\frac{dy}{dx}=\frac{dy}{d\theta }\times \frac{d\theta }{dx}$

$\sin \theta \times \frac{1}{-\cos \theta }=-\tan \theta$

For , $\theta =\frac{\pi }{4}$

$⟹-\tan \frac{\pi }{4}$

$⟹-1$