Practice Flashcards
Flip to reveal answersExpand sin(A + B).
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 8 Flashcards — Compound angle identities
Sign up free to track progress and get spaced-repetition review schedules.
Question
Expand sin(A + B).
Answer
sin A cos B + cos A sin B (same sign as the bracket; terms cross over).
Question
Expand cos(A − B).
Answer
cos A cos B + sin A sin B (terms match up; the middle sign FLIPS, so a − bracket gives a +).
Question
Why does cos(A + B) have a MINUS in the middle?
Answer
The cos formula always flips the middle sign relative to the bracket: cos(A+B) = cos A cos B − sin A sin B.
Question
Expand tan(A + B).
Answer
(tan A + tan B)/(1 − tan A tan B). The bottom sign is the opposite of the top.
Question
State tan 2A and where it comes from.
Answer
tan 2A = 2 tan A/(1 − tan²A); put B = A in tan(A+B).
Question
Find sin 75° exactly.
Answer
sin(45°+30°) = (√6 + √2)/4.
Question
Find tan 75° exactly.
Answer
tan(45°+30°) = (√3+1)/(√3−1) = 2 + √3 after rationalising.
Question
How do you SOLVE an equation like sin(x + π/6) = cos x?
Answer
Expand the bracket with sin(A+B), gather terms into one ratio (here tan x = 1/√3), then list all solutions in the interval.
Read the notes
Full study notes for Compound angle identities
Topic 3.10 hub
Compound angles (HL only)
More from Topic 3.10
All flashcards in this topic
Math AA exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free