Derivative of trigonometric function Cosecx and secx

DERIVATE OF 'cosecx'
Let y=cosecx……. i

Then,

Now,
       Subtracting i from ii we get,

By the first principle,

DERIVATE OF 'secx'

Let y=secx……. i

Then,

Now,
       Subtracting i from ii we get,

By the first principle,