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101.
Product of sine and cosine
sin⁡α⋅cos⁡β=12[sin⁡(α−β)+sin⁡(α+β)]\sin\alpha \cdot \cos \beta = \dfrac{1}{2} \left[ \sin(\alpha-\beta) + \sin(\alpha + \beta) \right]
Trigonometry
102.
Product of tangents
tan⁡α⋅tan⁡β=tan⁡α+tan⁡βcot⁡α+cot⁡β\tan\alpha \cdot \tan\beta = \dfrac{\tan \alpha + \tan \beta}{\cot \alpha + \cot \beta}
Trigonometry
103.
Product of cotangents
cot⁡α⋅cot⁡β=cot⁡α+cot⁡βtan⁡α+tan⁡β\cot\alpha \cdot \cot\beta = \dfrac{\cot \alpha + \cot \beta}{\tan \alpha + \tan \beta}
Trigonometry
104.
Product of tangent and cotangents
tan⁡α⋅cot⁡β=tan⁡α+cot⁡βcot⁡α+tan⁡β\tan\alpha \cdot \cot\beta = \dfrac{\tan\alpha + \cot\beta}{\cot\alpha+\tan\beta}
Trigonometry
105.
A⊂IA \sub I
Sets
106.
A⊂AA \sub A
Sets
107.
Empty set
∅⊂A\emptyset \sub A
Sets
108.
Union of sets
A∪B={x:x∈A  or  x∈B}A \cup B= \{x : x \in A \; \text{or} \; x \in B \}
Sets
109.
Intersection of sets
A∩B={x:x∈A  and  x∈B}A \cap B= \{x : x \in A \; \text{and} \; x \in B \}
Sets
110.
Difference of sets
A∖B={x:x∈A and x∉B}A \setminus B = \{ x : x\in A \, \text{and} \, x\notin B\}
Sets
111.
Set commutativity
A∪B=B∪AA \cup B = B \cup A
Sets
112.
Set commutativity
A∩B=B∩AA \cap B = B \cap A
Sets
113.
Set associativity
A∪(B∪C)=(A∪B)∪CA \cup \left(B \cup C \right) = \left( A \cup B \right) \cup C
Sets
114.
Set associativity
A∩(B∩C)=(A∩B)∩CA \cap \left(B \cap C \right) = \left( A \cap B \right) \cap C
Sets
115.
Set distributivity
A∪(B∩C)=(A∪B)∩(A∪C)A \cup \left(B \cap C\right) = \left(A \cup B \right) \cap \left(A \cup C \right)
Sets
116.
Set distributivity
A∩(B∪C)=(A∩B)∪(A∩C)A \cap \left(B \cup C\right) = \left(A \cap B \right) \cup \left(A \cap C \right)
Sets
117.
Idempotency
A∪A=AA \cup A = A
Sets
118.
Idempotency
A∩A=AA \cap A = A
Sets
119.
Domination
A∩∅=AA \cap \empty = A
Sets
120.
Domination
A∪I=IA \cup I = I
Sets

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