Question

sinθ+cosθ=√2 求tanθ+1÷tanθ

sinθ+cosθ=√2 求sin3次方θ－cos3次方θ 谢

Answer 1

sinθ+cosθ=√2
两边平方
1+2sinθcosθ=2
sinθcosθ=1/2
tanθ+1÷tanθ
=sinθ/cosθ+cosθ/sinθ
=（sin²θ+cos²θ）/(cosθsinθ)
=1/(1/2)
=2

Answer 2

sinθ+cosθ
=根号下2(根号下2sinθ/2+根号下2cosθ/2)
=根号下2sin(θ+π/4)<=根号下2
当θ+π/4=π/2时 根号下2sin(θ+π/4)=根号下2
所以θ=π/4 tanθ+1/tanθ=tanπ/4+1/tanπ/4=1+1=2