Question

这三道数学题怎么做？

1、化简sin50°(1+√3tan10°）
2、已知sin(α+β）=1/2，sin(α-β）=1/3，求tanα/tanβ
3、cos2π/7 * cos4π/7 * cos6π/7=？

Answer 1

1、原式=2sin50(1/2 *cos10 + +√3/2 *sin10)/cos10
=2sin50(sin30cos10+cos30sin10)/cos10
=2sin50sin40/cos10
=2sin50cos50/cos10
=sin100/cos10
=cos10/c0s10
=1

2、sin(α+β）=1/2 sinαcosβ+cosαsinβ=1/2
sin(α-β）=1/3 sinαcosβ-cosαsinβ=1/3
sinαcosβ=5/12
cosαsinβ=1/12
tanα/tanβ=sinαcosβ/cosαsinβ=5

3、原式=-cosπ/7 * cos2π/7 * cos4π/7
=(-2sinπ/7*cosπ/7*cos2π/7*cos4π/7)/2sinπ/7
=(-2sin2π/7*cos2π/7*cos4π/7)/4sinπ/7
=(-2sin4π/7*cos4π/7)/8sinπ/7
=-sin8π/7)/8sinπ/7
=sinπ/7)/8sinπ/7
=1/8