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Cosine of a Sum
cos even: cos(-B)=cos B. sin odd: sin(-B)=-sin B. So the + in the difference law becomes a - between the sin product.
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Cosine of a Sum
What is it?
cos even: cos(-B)=cos B. sin odd: sin(-B)=-sin B. So the + in the difference law becomes a - between the sin product.
In simple words
- cos even: cos(-B)=cos B.
- cos(A+B)
- Check A=B: cos 2A = cos2-sin2
- State the rule, show the working, and check the answer.
Important terms
COSINE OF A SUM: cos even: cos(-B)=cos B. sin odd: sin(-B)=-sin B. So the + in the difference law becomes a - between the sin product.
COS(A+B): cos even: cos(-B)=cos B.
What you should learn
- State the rule or meaning of cosine of a sum in easy words.
- Apply cosine of a sum in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Examples
- cos(A+B)
- Check A=B: cos 2A = cos2-sin2
- Keep the minus
MAIN IDEA
cos even: cos(-B)=cos B. sin odd: sin(-B)=-sin B. So the + in the difference law becomes a - between the sin product.
EXAM USE
Write the rule first: cos even: cos(-B)=cos B. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Recommended for Class 11
Full school-level explanation
cos even: cos(-B)=cos B. sin odd: sin(-B)=-sin B. So the + in the difference law becomes a - between the sin product.
Understand the idea, then apply it:
WHAT — COSINE OF A SUM
cos even: cos(-B)=cos B. sin odd: sin(-B)=-sin B. So the + in the difference law becomes a - between the sin product.
WHY — Why it matters
This rule is a separate learning unit inside compound angles: cos and sin of sums. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: cos even: cos(-B)=cos B. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
MAIN IDEA
cos even: cos(-B)=cos B. sin odd: sin(-B)=-sin B. So the + in the difference law becomes a - between the sin product.
Remember
- even/odd
Examples
- cos(A+B)
- Check A=B: cos 2A = cos2-sin2
- Keep the minus
EXAM USE
Write the rule first: cos even: cos(-B)=cos B. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Remember
- focused answer
- accurate support
Examples
- State the central idea
- Use one accurate detail
- Check the final response
How to answer a cosine of a sum question
How it works
- Read the exact command word and identify what the question asks.
- State the matching idea, rule, or meaning before adding detail.
- Use the unit evidence or mathematical working that directly supports the answer.
- Check accuracy, relevance, and answer length before finishing.
Remember
- even/odd
- cos(A+B)=cos A cos B - sin A sin B
- sin(A+B)=sin A cos B + cos A sin B
- sine plus, cosine minus
- even/odd
- focused answer
- accurate support
- even/odd
Deeper understanding
Go beyond memorising Cosine of a Sum. Connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
Core Idea
What to Know
Example or Evidence
How to Answer
Exam focus
Quick revision
- even/odd
- cos(A+B)=cos A cos B - sin A sin B
- sin(A+B)=sin A cos B + cos A sin B
- sine plus, cosine minus
- COSINE OF A SUM: cos even: cos(-B)=cos B. sin odd: sin(-B)=-sin B. So the + in the difference law becomes a - between
- COS(A+B): cos even: cos(-B)=cos B.
sin(A+B) is plus both. cos(A+B) is minus on the sin product.
For long answers on Cosine of a Sum: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- even/odd
- cos(A+B)=cos A cos B - sin A sin B
- sin(A+B)=sin A cos B + cos A sin B
- sine plus, cosine minus
Important formulas
- even/odd
- cos(A+B)=cos A cos B - sin A sin B
- sin(A+B)=sin A cos B + cos A sin B
Common exam traps
- sin(A+B) is plus both. cos(A+B) is minus on the sin product.
- Do not choose a formula before checking that its conditions fit the question.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
sin(A+B) is plus both. cos(A+B) is minus on the sin product.
- Mistake
Do not choose a formula before checking that its conditions fit the question.
- Mistake
Do not hide sign changes, restrictions, or skipped algebra steps.
- Mistake
sin(A+B) is plus both. cos(A+B) is minus on the sin product.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
even/odd
cos(A+B)=cos A cos B - sin A sin B
sin(A+B)=sin A cos B + cos A sin B
sine plus, cosine minus
cos even: cos(-B)=cos B. sin odd: sin(-B)=-sin B. So the + in the difference law becomes a - between the sin product.
cos(A+B)=cos A cos B - sin A sin B
- Definition
- cos even: cos(-B)=cos B. sin odd: sin(-B)=-sin B. So the + in the difference law becomes a - between the sin product.
- Formula
- cos(A+B)=cos A cos B - sin A sin B
- Example
- cos(A+B)
- Critical warning
- sin(A+B) is plus both. cos(A+B) is minus on the sin product.
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Exam Practice
Define
Q1. Define Cosine of a Sum.
Explain
Q2. Explain: MAIN IDEA.
Example
Q3. Give one clear example of Cosine of a Sum and say why it fits.
Mistake
Q4. State one common mistake students make about Cosine of a Sum.
Exam note
Q5. Write a short exam note on Cosine of a Sum: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.