根号3tan(pai/6-θ)tan(pai/6+θ)+tan(pai/6-θ)+tan(pai/6+θ)=?根3*tan(pai/6-θ)*tan(pai/6+θ)+tan(pai/6-θ)+tan(pai/6+θ)=?用三角的恒等变换
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 00:04:42
![根号3tan(pai/6-θ)tan(pai/6+θ)+tan(pai/6-θ)+tan(pai/6+θ)=?根3*tan(pai/6-θ)*tan(pai/6+θ)+tan(pai/6-θ)+tan(pai/6+θ)=?用三角的恒等变换](/uploads/image/z/2668326-6-6.jpg?t=%E6%A0%B9%E5%8F%B73tan%28pai%2F6-%CE%B8%EF%BC%89tan%28pai%2F6%2B%CE%B8%EF%BC%89%2Btan%28pai%2F6-%CE%B8%EF%BC%89%2Btan%28pai%2F6%2B%CE%B8%29%3D%3F%E6%A0%B93%2Atan%28pai%2F6-%CE%B8%EF%BC%89%2Atan%28pai%2F6%2B%CE%B8%EF%BC%89%2Btan%28pai%2F6-%CE%B8%EF%BC%89%2Btan%28pai%2F6%2B%CE%B8%29%3D%3F%E7%94%A8%E4%B8%89%E8%A7%92%E7%9A%84%E6%81%92%E7%AD%89%E5%8F%98%E6%8D%A2)
根号3tan(pai/6-θ)tan(pai/6+θ)+tan(pai/6-θ)+tan(pai/6+θ)=?根3*tan(pai/6-θ)*tan(pai/6+θ)+tan(pai/6-θ)+tan(pai/6+θ)=?用三角的恒等变换
根号3tan(pai/6-θ)tan(pai/6+θ)+tan(pai/6-θ)+tan(pai/6+θ)=?
根3*tan(pai/6-θ)*tan(pai/6+θ)+tan(pai/6-θ)+tan(pai/6+θ)=?
用三角的恒等变换
根号3tan(pai/6-θ)tan(pai/6+θ)+tan(pai/6-θ)+tan(pai/6+θ)=?根3*tan(pai/6-θ)*tan(pai/6+θ)+tan(pai/6-θ)+tan(pai/6+θ)=?用三角的恒等变换
tan(π/6-θ) =[ tanπ/6-tanθ]/(1+tanπ/6tanθ)
= [1/√3 - tanθ]/(1+tanθ/√3)
= (1-√3tanθ)/(√3+tanθ)
tan(π/6+θ) =(1+√3tanθ)/(√3-tanθ)
√3tan(π/6-θ)tan(π/6+θ)+tan(π/6-θ)+tan(π/6+θ)
=√3[(1-√3tanθ)/(√3+tanθ)][(1+√3tanθ)/(√3-tanθ)]+(1+√3tanθ)/(√3-tanθ)+ (1-√3tanθ)/(√3+tanθ)
=√3(1-3(tanθ)^2)/(3-(tanθ)^2) +[(1+√3tanθ)(√3+tanθ)+(1-√3tanθ)(√3-tanθ)]/(3-(tanθ)^2)
=[√3(1-3(tanθ)^2) + 2√3+2√3(tanθ)^2 ] /(3-(tanθ)^2)
= √3(3-(tanθ)^2) /(3-(tanθ)^2)
= √3