Question

cos二倍角公式推导

cos二倍角公式的推导
余弦二倍角
1.Cos2α=1-2Sinα^2
2.Cos2a=2Cosa^2-1
是如何推到出来的?

Answer 1

Cos2α=cos(α+α)
=cosαcosα-sinαsinα
=cos^2α-sin^2α
=1-sin^2α-sin^2α
=1-2Sinα^2
Cos2α=cos(α+α)
=cosαcosα-sinαsinα
=cos^2α-sin^2α
=cos^2α-(1-cos^2α)
=2cos^2α-1