Need help with this set proof question

[Bigb600]

P={a/c |a,c ∈ N and a2+b2=c2 for some b N }
T= {x∈R|sin(x)∈P}
C= {x∈R|cos(x)∈Q}

Prove that T is a subset of C. You will need Pythagorean identity ( sin^2(x) + cos^2(x)=1)

 

[Steven G]

I like how you told us what we will need to solve your problem. Being polite will not get you your answer, sorry.

On this forum we want the student to solve their own problem with helpful hints from the helpers on the forum. This means that you need to be actively involved in finding the solution. You need to post a problem without any errors (your problem does contain errors) and tell us where you are stuck and what help you need. You can accomplish this by showing us your work. Please post back.

Here is a hint of how to do this problem. Pick an arbitrary element x in T and show that x is in C. Then conclude that T is a subset of C