Question

Can you please help me verify these?
>sin7x-sin5x= tanx(cos7x-cos5x)
>(1-cosx)cot(1/2x) = sinx
>1+tanx tan(x/2) = secx

Its very confusing because of all the double-half angle formulas >_<

Answer 1

I tried your #1 with x=10° and it did not work
so it is not even an identity

#2 and #3.
you will have to remember that
cos 2A = 1 - 2sin^2 A , and sin 2A = 2sinAcosA

or

cosx = 1 - 2sin^2 (x/2) , and sinx = 2sin(x/2)cos(x/2)