# Question: given the set a x cosx 0...

###### Question details

Given the set A = {x : cos(x) = 0} prove the following:

(a) If B = {π, 3π, 5π,−π,−3π} then B ⊂ A.

(b) IfC= {x:sin(x)=1} thenC⊂A.

(c) If D = {π + kπ,k ∈ Z} then D = A. (Recall, you must show two separate statements: A ⊆ D and D ⊆ A.)

(d) If E= {x:cot(x)=1} then E∩ A=∅.

Please write as full proofs.