Addition and Double-angle Formulae
Select and apply the supplied sine and cosine addition or double-angle identities with correct signs.
How to study Higher Mathematics
Practise a skill without a calculator first, connect it to neighbouring techniques, then apply it in unfamiliar contexts with complete working and interpretation.
Core concepts
Concept 1
sin(A ± B)
Exam cue: Which supplied identity matches the target expression?
Concept 2
cos(A ± B)
Exam cue: Which sign changes in the cosine addition formula?
Concept 3
sin 2A
Exam cue: Which cos 2A form best fits the available information?
Concept 4
cos 2A forms
Concept 5
exact values
Risk pitfalls and guardrails
Using the sine sign pattern for cosine
Guardrail: Check signs, brackets, domain restrictions, units and whether the answer needs justification.
Confusing sin 2A with 2 sin A
Guardrail: Check signs, brackets, domain restrictions, units and whether the answer needs justification.
Choosing an inefficient double-angle form
Guardrail: Check signs, brackets, domain restrictions, units and whether the answer needs justification.
Memory anchors
Sine keeps the sign
sin(A ± B) uses the same middle sign.
Cosine flips the sign
cos(A ± B) uses the opposite middle sign.
Double sine is a product
sin 2A = 2 sin A cos A.
Three cosine options
Use cos²A − sin²A, 2cos²A − 1 or 1 − 2sin²A.
Formula list is supplied
Read it accurately instead of relying on a fragile memory.
Exact stays exact
Retain surds and fractions unless approximation is requested.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Expand sin(A+B).
Expand cos(A−B).
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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