How can we prove the derivative of tan(y/2) is 2/(1 + x²)?

[thomas49th]

Prove:

$$\frac{Sec^{2}\frac{y}{2}}{2} \eqiv \frac{2}{1+x^{2}}$$

Well i know from the pythagorean identities that tan^{2}x + 1 = sec^{2}x
so

$$\frac{tan^{2}\frac{y}{2} + 1}{2} \eqiv \frac{2}{1+x^{2}}$$

But now I am stuck!

If your interested the full qusetion is page 35, question 7 (ii) here:

http://www.edexcel.org.uk/VirtualContent/105484/GCE_Pure_Maths_C1_C4_Specimen_Paper_MkScheme.pdf

Can someone point me in the right direction

Cheerz

 

[tiny-tim]

The actual question is:

Given that x = tan(y/2), prove that dy/dx = 2/(1 + x²).​

thomas49th, just differentiate both sides of x = tan(y/2).