Question

已知sinθ-cosθ=√2/3(0<θ<π/2),求sinθ+cosθ的值

求过程 谢谢！

Answer 1

解

sinθ-cosθ=√2/3
两边平方得：
sin²θ+cos²θ-2sinθcosθ=2/9
即1-sin2θ=2/9
∴sin2θ=7/9
∵0<θ<π/2
∴sinθ>0.cosθ>0
∴sinθ+cosθ>0
∴sinθ+cosθ
=√(sinθ+cosθ)²
=√1+2sinθcosθ
=√1+sin2θ
=√1+7/9
=√16/9
=4/3

Answer 2

sinθ-cosθ=√2/3
两边平方
1-2sinθcosθ=2/9
2sinθcosθ=7/9

sinθ+cosθ
=根号(sinθ+cosθ)²
=根号(1+2sinθcosθ)
=根号(1+7/9)
=根号(16/9)
=4/3