Question

已知sinα+cosα=4/5，则sin2α=

Answer 1

sinα+cosα=4/5，
平方得
1+2sinαcosα=16/25
则sin2α=-9/25

追问

sin65°+sin15°sin10°/sin25°-cos25°cos80°=
log2为底cosπ/9+log2为底cos2π/9+log2为底cos4π/9=

追答

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3

log2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

Answer 2

sin2a=2sinacosa
2sinacosa=（sina+cosa）²-（sin²a+cos²a）
=16/25-1
=-9/25
所以 sin2a=-9/25

追问

sinθ+sin2θ/1+cosθ+cos2θ=

Answer 3

sinα+cosα的平方= sina^2+cosa^2 +2sinacosa = 1+sin2a = 16/25
sin2a=-9/25