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101.
Product of sine and cosine
$\sin\alpha \cdot \cos \beta = \dfrac{1}{2} \left[ \sin(\alpha-\beta) + \sin(\alpha + \beta) \right]$
Trigonometry
102.
Product of tangents
$\tan\alpha \cdot \tan\beta = \dfrac{\tan \alpha + \tan \beta}{\cot \alpha + \cot \beta}$
Trigonometry
103.
Product of cotangents
$\cot\alpha \cdot \cot\beta = \dfrac{\cot \alpha + \cot \beta}{\tan \alpha + \tan \beta}$
Trigonometry
104.
Product of tangent and cotangents
$\tan\alpha \cdot \cot\beta = \dfrac{\tan\alpha + \cot\beta}{\cot\alpha+\tan\beta}$
Trigonometry
105.
$A \sub I$
Sets
106.
$A \sub A$
Sets
107.
Empty set
$\emptyset \sub A$
Sets
108.
Union of sets
$A \cup B= \{x : x \in A \; \text{or} \; x \in B \}$
Sets
109.
Intersection of sets
$A \cap B= \{x : x \in A \; \text{and} \; x \in B \}$
Sets
110.
Difference of sets
$A \setminus B = \{ x : x\in A \, \text{and} \, x\notin B\}$
Sets
111.
Set commutativity
$A \cup B = B \cup A$
Sets
112.
Set commutativity
$A \cap B = B \cap A$
Sets
113.
Set associativity
$A \cup \left(B \cup C \right) = \left( A \cup B \right) \cup C$
Sets
114.
Set associativity
$A \cap \left(B \cap C \right) = \left( A \cap B \right) \cap C$
Sets
115.
Set distributivity
$A \cup \left(B \cap C\right) = \left(A \cup B \right) \cap \left(A \cup C \right)$
Sets
116.
Set distributivity
$A \cap \left(B \cup C\right) = \left(A \cap B \right) \cup \left(A \cap C \right)$
Sets
117.
Idempotency
$A \cup A = A$
Sets
118.
Idempotency
$A \cap A = A$
Sets
119.
Domination
$A \cap \empty = A$
Sets
120.
Domination
$A \cup I = I$
Sets

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