In ECET 2026, Mathematics is a high-scoring section for CSE diploma students. Compound Angle Formulas are formula-based questions that appear frequently in APECET and TSECET papers. Memorizing these formulas and practicing MCQs can help you score quick marks without lengthy calculations.
📘 Concept Notes – Compound Angle Formulas
Definition: Compound angles are angles formed by the sum or difference of two or more angles. The trigonometric values can be calculated using special formulas.
📐 Key Formulas
Sine Formulas:
![\[\sin(A + B) = \sin A \cos B + \cos A \sin B\]](https://learnnewthings.fun/wp-content/ql-cache/quicklatex.com-6787babf14483e879dc7c7091b686a1e_l3.png "Rendered by QuickLaTeX.com")
![\[\sin(A - B) = \sin A \cos B - \cos A \sin B\]](https://learnnewthings.fun/wp-content/ql-cache/quicklatex.com-ee4cffa2444e0ae058b0807a9575978e_l3.png "Rendered by QuickLaTeX.com")
Cosine Formulas:
![\[\cos(A + B) = \cos A \cos B - \sin A \sin B\]](https://learnnewthings.fun/wp-content/ql-cache/quicklatex.com-5b8c63c21e1eb5fe2ee45543c6a6c254_l3.png "Rendered by QuickLaTeX.com")
![\[\cos(A - B) = \cos A \cos B + \sin A \sin B\]](https://learnnewthings.fun/wp-content/ql-cache/quicklatex.com-4702422798532ec8ac37b6bf3bfe883b_l3.png "Rendered by QuickLaTeX.com")
Tangent Formulas:
![\[\tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}\]](https://learnnewthings.fun/wp-content/ql-cache/quicklatex.com-dbf59cfaa7cd279ab9b88a7824688872_l3.png "Rendered by QuickLaTeX.com")
![\[\tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}\]](https://learnnewthings.fun/wp-content/ql-cache/quicklatex.com-81ec3be75cd290154b1577a84bc15809_l3.png "Rendered by QuickLaTeX.com")
🧠 Key Points:
- Always check angles are in same units (degrees/radians).
- Tangent formulas are undefined if denominator = 0.
- Commonly used in elevation, depression, and multiple angle problems.
🔟 10 Most Expected MCQs
Q1. Evaluate
![\[\sin 60^\circ \cos 30^\circ + \cos 60^\circ \sin 30^\circ\]](https://learnnewthings.fun/wp-content/ql-cache/quicklatex.com-4e4053d3f1709976c2cf3e921a4ca1b0_l3.png "Rendered by QuickLaTeX.com")
A)
B) 
C) 
D) 
Q2. Formula for 
is:
A) 
B) 
C) 
D) 
Q3. 
is equal to:
A) B) C) D)
Q4. Evaluate
![\[\tan 45^\circ + \tan 45^\circ\]](https://learnnewthings.fun/wp-content/ql-cache/quicklatex.com-b0f818400b43ee90cfdcdd6d9dbcad71_l3.png "Rendered by QuickLaTeX.com")
A)
B) 
C) 
D) Undefined
Q5. Evaluate
![\[\cos 90^\circ \cos 30^\circ - \sin 90^\circ \sin 30^\circ\]](https://learnnewthings.fun/wp-content/ql-cache/quicklatex.com-9c82b06dc5a4a7d91b49108593340c5e_l3.png "Rendered by QuickLaTeX.com")
A)
B) 
C) D)
Q6. Formula for 
is:
A) 
B) 
C) 
D) 
Q7. Evaluate
![\[\sin 45^\circ \cos 45^\circ + \cos 45^\circ \sin 45^\circ\]](https://learnnewthings.fun/wp-content/ql-cache/quicklatex.com-b93621119b2f7c6ffa450c1f74802b1c_l3.png "Rendered by QuickLaTeX.com")
A) 0 B) 1 C)
D)
Q8. Formula for 
is:
A) B) C) D)
Q9. Evaluate
![\[\tan(60^\circ - 45^\circ)\]](https://learnnewthings.fun/wp-content/ql-cache/quicklatex.com-c8e63038da80ce3a6c31cfe09abac636_l3.png "Rendered by QuickLaTeX.com")
A) 1 B)
C) 
D) 0
Q10. Formula for 
is:
A) B) C) D)
✅ Answer Key
| Q.No | Answer |
|---|---|
| Q1 | A |
| Q2 | B |
| Q3 | A |
| Q4 | D |
| Q5 | C |
| Q6 | C |
| Q7 | C |
| Q8 | A |
| Q9 | B |
| Q10 | B |
🧠 Explanations
Q1 → A: 
Q2 → B: Direct formula: 
Q3 → A: Direct formula: 
Q4 → D: Denominator becomes zero → Undefined
Q5 → C: Expression equals 
Q6 → C: 
Q7 → C: Equals 
Q8 → A: Direct formula
Q9 → B: Using tan subtraction formula
Q10 → B: 
🎯 Why This Practice Matters
Compound Angle Formulas are direct formula-based questions in ECET. Memorizing formulas and practicing MCQs ensures quick problem-solving and improves Mathematics scores.
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