Verify that the trigonometric equation is an identity. 1/2 sin 2 x − sin^2x over sinxcos2x = 1 over sinx+cosx

Question

Verify that the trigonometric equation is an identity.
cotx over 1-sinx =secx(cscx+1)

Can someone please Help!!! these are so hard for me to understand

Thank you

Answer 1

#1 The LS can be written as

        sinx(cosx-sinx)
----------------------------------
sinx(cosx+sinx)(cosx-sinx)

I think it's clear what comes next ...

For #2, on the LS, multiply top and bottom by (1+sinx) and I think it will come clear.

Answer 2

I stil do not understand problem two