1、化简 (tan2π-θ)sin(-2π-θ)cos(6π-θ)/cos(θ-π)sin(5π+θ)2、化简 sin(15π/2+α)cos(α-π/2)/sin(9π/2-α)cos(3π/2+α) 3、求证 sin(π/2+θ)-cos(π-θ)/sin(π/2-θ)-sin(π-θ)=2
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![1、化简 (tan2π-θ)sin(-2π-θ)cos(6π-θ)/cos(θ-π)sin(5π+θ)2、化简 sin(15π/2+α)cos(α-π/2)/sin(9π/2-α)cos(3π/2+α) 3、求证 sin(π/2+θ)-cos(π-θ)/sin(π/2-θ)-sin(π-θ)=2](/uploads/image/z/758606-14-6.jpg?t=1%E3%80%81%E5%8C%96%E7%AE%80+%28tan2%CF%80-%CE%B8%29sin%28-2%CF%80-%CE%B8%29cos%286%CF%80-%CE%B8%29%EF%BC%8Fcos%EF%BC%88%CE%B8-%CF%80%EF%BC%89sin%EF%BC%885%CF%80%2B%CE%B8%EF%BC%892%E3%80%81%E5%8C%96%E7%AE%80+sin%EF%BC%8815%CF%80%EF%BC%8F2%2B%CE%B1%EF%BC%89cos%EF%BC%88%CE%B1-%CF%80%EF%BC%8F2%EF%BC%89%EF%BC%8Fsin%EF%BC%889%CF%80%EF%BC%8F2-%CE%B1%EF%BC%89cos%EF%BC%883%CF%80%EF%BC%8F2%2B%CE%B1%EF%BC%89+3%E3%80%81%E6%B1%82%E8%AF%81+sin%EF%BC%88%CF%80%EF%BC%8F2%2B%CE%B8%EF%BC%89-cos%EF%BC%88%CF%80-%CE%B8%EF%BC%89%EF%BC%8Fsin%EF%BC%88%CF%80%EF%BC%8F2-%CE%B8%EF%BC%89-sin%EF%BC%88%CF%80-%CE%B8%EF%BC%89%3D2)
1、化简 (tan2π-θ)sin(-2π-θ)cos(6π-θ)/cos(θ-π)sin(5π+θ)2、化简 sin(15π/2+α)cos(α-π/2)/sin(9π/2-α)cos(3π/2+α) 3、求证 sin(π/2+θ)-cos(π-θ)/sin(π/2-θ)-sin(π-θ)=2
1、化简 (tan2π-θ)sin(-2π-θ)cos(6π-θ)/cos(θ-π)sin(5π+θ)
2、化简 sin(15π/2+α)cos(α-π/2)/sin(9π/2-α)cos(3π/2+α)
3、求证 sin(π/2+θ)-cos(π-θ)/sin(π/2-θ)-sin(π-θ)=2/1-tanθ
1、化简 (tan2π-θ)sin(-2π-θ)cos(6π-θ)/cos(θ-π)sin(5π+θ)2、化简 sin(15π/2+α)cos(α-π/2)/sin(9π/2-α)cos(3π/2+α) 3、求证 sin(π/2+θ)-cos(π-θ)/sin(π/2-θ)-sin(π-θ)=2
(tan2π-θ)sin(-2π-θ)cos(6π-θ)/cos(θ-π)sin(5π+θ)
=(-tanθ)(-sinθ)cosθ/(-cosθ)(-sinθ)
=tanθsinθcosθ/cosθsinθ
=tanθ
sin(15π/2+α)cos(α-π/2)/sin(9π/2-α)cos(3π/2+α)
=sin(8π-π/2+α)cos(π/2-α)/sin(4π+π/2-α)cos(3π/2+α)
=sin(-π/2+α)cos(π/2-α)/sin(π/2-α)cos(3π/2+α)
=[-sin(π/2-α)]cos(π/2-α)/sin(π/2-α)cos(3π/2+α)
=[-cosα]sinα/cosαsinα
=-1
[sin(π/2+θ)-cos(π-θ)]/[sin(π/2-θ)-sin(π-θ)]
=(cosθ+cosθ)/(cosθ-sinθ)
=2cosθ/(cosθ-sinθ)(分子分母同时除以cosθ)
=(2cosθ/cosθ)/(cosθ/cosθ-sinθ/cosθ)
=2/(1-tanθ)
1.tan(2π-b)sin(-2π-b)cos(6π-b)/(cos(b-π)sin(5π+b))
=tan(-b)sin(-b)cos(-b)/(cos(π-b)sin(4π+π+b))
=sin(-b)/cos(-b).sin(-b)cos(-b)/(-cosb.(-sinb))
=sinb.sinb/(cosbsinb)
=tanb
tan(2π-θ)=-tanθ,sin(-2π-θ)=-sinθ,cos(6π-θ)=cosθ,cos(θ-π)=-cosθ,sin(5π+θ)=-sinθ.
所以(tan2π-θ)sin(-2π-θ)cos(6π-θ)/cos(θ-π)sin(5π+θ)=-tanθ