Question

Prove that `(1+secx)/tanx=cot(x/2)`?

Answer 1

`LHS=(1+secx)/tanx`

`=(1+1/cosx)/tanx`

`=((1+cosx)/cancel(cosx))/(sinx/cancel(cosx))`

`=(1+cosx)/sinx`

`=(2cos^2(x/2))/(2sin(x/2)*cos(x/2))=cot(x/2)=RHS`