sinα+cosα=4/5,
平方得
1+2sinαcosα=16/25
则sin2α=-9/25sin65°+sin15°sin10°/sin25°-cos25°cos80°=log2为底cosπ/9+log2为底cos2π/9+log2为底cos4π/9=问我这么多，好。疑似错了。已经修正sin65°+sin15°sin10°/sin25°-cos15°cos80°=(sin(75°-10°)+cos75°sin10°)/（cos65°-cos15°cos80°）=sin75°cos10°/sin15°sin80°=tan75°=tan(45°+30°)=2+根号3log2为底cosπ/9+log2为底cos2π/9+log2为底cos4π/9=log2为底（cosπ/9cos2π/9cos4π/9）因为cosπ/9cos2π/9cos4π/9=(sinπ/9cosπ/9cos2π/9cos4π/9)/sinπ/9=(sin8π/9)/(8sinπ/9)=1/8所以原式=-3