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secondary 4 | A Maths

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pls help me with (b) :))

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)