Okay. Just to make sure, cot x = cos x / sin x.
1) So, once cot x is distributed to sin x, then the sin x will cancel out the sin x from the cot x (which I showed you above) and you will be left with just cos x.
2) Once cot x is distributed to sec x (which can be also written as 1 / cos x), the cos x from cot x will cancel out the cos x from sec x.
3) Once you do that, your final answer will be: cos x + (1 / sin x )