Consider the following for the two (02) items that follow: Let $p=|\sin \alpha -\sin (\alpha -90{}^{\circ })|$.

What is the minimum value of p?

Consider the following for the two (02) items that follow: Let $p=|\sin \alpha -\sin (\alpha -90{}^{\circ })|$.

What is the maximum value of p?

Consider the following for the three (03) items that follow:
Let p = tan 2α   - tanα and q = cotα - cot 2α

What is (p/q) equal to?

Consider the following for the three (03) items that follow:
Let p = tan 2α   - tanα and q = cotα - cot 2α

What is $(p+q)$ equal to?