verify algebraically

(1+csc x)/(cot x+cos X)=sec x

\frac{1+csc(x)}{cot(x)+cos(x)}=sec(x)

Start by putting it all in terms of sine and cosine.

\frac{1+\frac{1}{sin(x)}}{\frac{cos(x)}{sin(x)}+co s(x)

Now, cross multiply and do some cancelling and it should become clear. Can you finish?