Sin(a+60)*sin(a-60)-sin(a)^2

Question

Sin(a+60)*sin(a-60)-sin(a)^2

Answer 1

Sinα*sinβ=(cos(α-β)-cos(α+β))/2
sin(α+60)*sin(α-60)-sin²α=(cos(α+60-α+60)-cos(α-60+α+60))/2-sin²α=
=(cos120-cos2α)/2-sin²α=(-sin30-(1-2sin²α))/2-sin²α=(-1/2-1+2sin²α)/2-sin²α=
=(-3/2+2sin²α)/2-sin²α=-3/4+sin²α-sin²α=-3/4=-0,75