Question

Differentiate y= 2tanx/2 prove that dy/dx= 2/1+cosx

Answer 1

y=2tanx/2
dy/dx=2sec^2x/2..1/2
=sec^2x/2
=1/cos^2x/2
cos^2x/2=1+cosx/2
put this value above
dy/dx=2/1+cosx

Answer 2

Given: y = 2 tan(x/2)

To prove: dy/dx = 2/(1+cos(x))

Proof: y = 2 tan(x/2)

dy/dx = 2× sec^(x/2) × (1/2)

dy/dx= sec^(1/2)

dy/dx= 1/(cos^(1/2)) [let eq 1]

As, cos^(x/2) = [1+ cos(x)]/ 2

Putting this in eq 1 we get,

dy/dx = 2/(1+cos(x))

Hence Proved.