Question

已知3π/2<θ<2π,试化简√(1+sinθ)—√(1—sinθ)

数学题

Answer 1

已知3π/2<θ<2π,3π/4<θ/2<π,sin(θ/2)>cos(θ/2),√(1+sinθ)—√(1—sinθ)= |sin(θ/2)+cos(θ/2)|—|sin(θ/2)-cos(θ/2)|= =sin(θ/2)+cos(θ/2)-sin(θ/2)+cos(θ/2)=2cos(θ/2).