Take this trigonometric function:

Using the chain rule i think it becomes:

But if we use the identity:

then the equation becomes

But if,

then,

Which doesn't appear so. Why am I getting different answers for the same derivative? Did I do something wrong in the above steps?

I accidentally took :

P.S. This is my first post and using [tex] is VERY slow and irritating, is there a faster way to insert math expressions