Question

if X = 2(theta + sin theta) and Y = 2(1- cos theta) , then value of dy/dx is​

Answer 1

Answer:

pls see the attachment

Answer 2

Answer:

The answer is tan(θ/2).

Explanation:

In the question, the value of X and Y is given in form of theta, and we need to find the derivative of y with respect to x. So, we can say that this is a parametric type of equation.

A parametric equation is a type of equation that uses an independent variable (in this case it is theta), and in which dependent variables are defined as the continuous function of the parameter and not dependent on any other existing variable.

X =2(θ + sin θ)

$\frac{dX}{d\theta} = 2(1 + Cos\theta)$  ( because the derivative of theta is 1 and sinθ is cosθ)

Y = 2(1-Cosθ)

$\frac{dY}{d\theta} =2(0+Sin\theta)=2Sin\theta$ (because the derivative of any constant is 0 and the derivative of Cosθ is -Sinθ)

Now we need to find dY/dX, so for this, we can do:-

$\frac{dY}{dX} = \frac{\frac{dY}{d\theta} }{\frac{dX}{d\theta} } =\frac{2Sin\theta}{2(1-Cos\theta)}$

$\frac{dY}{dX} = \frac{2sin\frac{\theta}{2}cos\frac{\theta}{2} }{2cos^2\frac{\theta}{2} } = tan\frac{\theta}{2}$

Therefore the solution is tan(θ/2).