Question

正切三角恒等变换公式

Answer 1

正切三角恒等变换公式：

cos(α+β)=cosα·cosβ-sinα·sinβ

sin(α-β)=sinα·cosβ-cosα·sinβ

tan(α+β)=(tanα+tanβ)/(1-tanα·tanβ)

sin(2α)=2sinα·cosα

cos(2α)=cos^2(α)-sin^2(α)=2cos^2(α)-1=1-2sin^2(α)

tan(2α)=2tanα/[1-tan^2(α)]

三倍角

sin3α = 3sinα-4sin³α

cos3α = 4cos³α-3cosα

tan3α = (3tanα-tan³α)/(1-3tan²α)

sin3α = 4sinα·sin(π/3-α)·sin(π/3+α)

cos3α = 4cosα·cos(π/3-α)·cos(π/3+α)

tan3α = tanα·tan(π/3-α)·tan(π/3+α)