Practice Flashcards
Expand sin(A + B).
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All Flashcards in Topic 3.10
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3.10.18 cards
Expand sin(A + B).
sin A cos B + cos A sin B (same sign as the bracket; terms cross over).
Expand cos(A − B).
cos A cos B + sin A sin B (terms match up; the middle sign FLIPS, so a − bracket gives a +).
Why does cos(A + B) have a MINUS in the middle?
The cos formula always flips the middle sign relative to the bracket: cos(A+B) = cos A cos B − sin A sin B.
Expand tan(A + B).
(tan A + tan B)/(1 − tan A tan B). The bottom sign is the opposite of the top.
State tan 2A and where it comes from.
tan 2A = 2 tan A/(1 − tan²A); put B = A in tan(A+B).
Find sin 75° exactly.
sin(45°+30°) = (√6 + √2)/4.
Find tan 75° exactly.
tan(45°+30°) = (√3+1)/(√3−1) = 2 + √3 after rationalising.
How do you SOLVE an equation like sin(x + π/6) = cos x?
Expand the bracket with sin(A+B), gather terms into one ratio (here tan x = 1/√3), then list all solutions in the interval.
Topic 3.10 study notes
Full notes & explanations for Compound angles (HL only)
Math AA exam skills
Paper structures, command terms & tips
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