Question

If x = a ($\theta +sin\theta )$ and y = a (1- cos$\theta$), then dy/dx will be equal to

• A. sin$\left(\frac{\theta }{2}\right)$
• B. cos$\left(\frac{\theta }{2}\right)$
• C. tan$\left(\frac{\theta }{2}\right)$
• D. cot$\left(\frac{\theta }{2}\right)$

Answer 1

The correct option is C tan$\left(\frac{\theta }{2}\right)$

x = a($\theta$ + sin$\theta$)

$\frac{dx}{d\theta }=a(1+cos\theta )$

y = a (1 - cos$\theta$)

$\frac{dy}{d\theta }=a(0+sin\theta )$

$\left(\frac{dy}{dx}\right)=\frac{sin\theta }{1+cos\theta }$

$=\frac{2sin\frac{\theta }{2}.cos\frac{\theta }{2}}{2co{s}^2\frac{\theta }{0}}=tan\frac{\theta }{2}$