Differentiation Question

[DeeRose]

Let y = 1 - cos x / 1 + cosx

Show that dy/dx = t+t^3 , where t = tan(x/2)​

 

[Deleted member 4993]

Let y = 1 - cos x / 1 + cosx

Show that dy/dx = t+t^3 , where t = tan(x/2)​

I am sure your problem should have been written as:


y = [1 - cos (x)] / [1 + cos(x)]

hint:

1 + cos(2Θ) = 2 * cos²(Θ)

1 - cos(2Θ) = 2 * sin²(Θ)

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[DeeRose]

When I use the quotient rule for 1 - cosx / 1 + cosx
I get 2sinx / (1+cosx)^2
Then that's where I'm stuck since I have to make dy/dx = t + t^3 , where t = tan(x/2)

 

[Deleted member 4993]

Now reduce that to proper form using half-angle formulae.