Question

sin164ºsin224º+sin254ºsin314º.sin﹙α+β﹚cos﹙γ-β﹚-cos﹙β+α﹚sin﹙β-γ﹚

sin﹙α-β﹚sin﹙β-γ﹚-cos﹙α-β﹚﹙γ-β﹚.﹙tan5π/4+tan5π/12﹚/1-tan5π/12. sin﹙α+β﹚-2sinαcosβ /2sinαsinβ+cos﹙α+β﹚化简 帮帮忙thankyou

Answer 1

sin164°sin224°+sin254°sin314°=-sin16°sin44°+cos16°cos44°=cos(44°+16°)=cos60°=1/2

sin(α+β)cos(γ-β)-cos(β+α)sin(β-γ)=sin(α+β)cos(β-γ)-cos(α+β)sin(β-γ)=sin(α+β-β+γ)=sin(α+γ)

(tan5π/4+tan5π/12)/(1-tan5π/12)=(tanπ/4+tan5π/12)/(1-tanπ/4tan5π/12)=tan(π/4+5π/12)=tan2π/3=-√3

[sin(α+β)-2sinαcosβ]/[2sinαsinβ+cos(α+β)]=(cosαsinβ-sinαcosβ)/(cosαcosβ+sinαsinβ)=sin(β-α)/cos(β-α)=tan(β-α)

Answer 2

你的题目没有看明白，太乱了，把题木拍下来在传上来

Answer 3

1/2