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secondary 4 | A Maths
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alice
Alice

secondary 4 chevron_right A Maths chevron_right Singapore

pls help me with (b) :))

Date Posted: 8 months ago
Views: 201
alice
Alice
8 months ago
ans is cos(2x) but my working is not getting near there
sstrike
Sstrike
8 months ago
(a)
sin(α+β)•cos(β) - cos(α+β)•sin(β)
= sin(α)•cos²(β)+cos(α)•sin(β)•cos(β)
- cos(α)•cos(β)•sin(β) + sin(α)•sin²(β)
= sin(α)

(b)
cos(x+y)•cos(x-y) - sin(x+y)•sin(x-y)
= cos²(x)•cos²(y) - sin²(x)•sin²(y)
- sin²(x)•cos²(y) + cos²(x)•sin²(y)
= cos²(x) - sin²(x)
= 2•cos²(x) - 1


P.S.
sin(a+b) = sin(a)•cos(b)+cos(a)•sin(b)
sin(a-b) = sin(a)•cos(b) - cos(a)•sin(b)

cos(a+b) = cos(a)•cos(b)-sin(a)•sin(b)
cos(a-b) = cos(a)•cos(b)+sin(a)•sin(b)