化简题及证明题请帮帮忙!1.化简:[1-tan²(x+y)]/2tan(x+y)2.证明 ①.(2sinα-s
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/17 17:59:30
化简题及证明题
请帮帮忙!
1.化简:[1-tan²(x+y)]/2tan(x+y)
2.证明 ①.(2sinα-sin2α)/2α+sin2α=tan² α/2
②.(1+sin2β )/sinβ+cosβ=sinβ+cosβ
③.sinθ(1+cos2θ)=sin2θcosθ
请帮帮忙!
1.化简:[1-tan²(x+y)]/2tan(x+y)
2.证明 ①.(2sinα-sin2α)/2α+sin2α=tan² α/2
②.(1+sin2β )/sinβ+cosβ=sinβ+cosβ
③.sinθ(1+cos2θ)=sin2θcosθ
1、因为tan2A=2tanA/(1-(tanA)^2)
则 [1-(tanA)^2)]/(2tanA)=1/tan2A
则 [1-tan²(x+y)]/2tan(x+y)=1/tan2(x+y).
2、(1)[题目抄写有错]
(2sinα-sin2α)/(2sinα+sin2α)
=2sinα(1-cosα)/[2sinα(1+cosα)]
=(1-cosα)/(1+cosα)
=tan² α/2
(2)(1+sin2β)/(sinβ+cosβ)
=(sinβ+cosβ)^2/(sinβ+cosβ)
=sinβ+cosβ.
(3)sinθ(1+cos2θ)
=sinθ*2(cosθ)^2
=(2sinθcosθ)cosθ
=sin2θcosθ.
则 [1-(tanA)^2)]/(2tanA)=1/tan2A
则 [1-tan²(x+y)]/2tan(x+y)=1/tan2(x+y).
2、(1)[题目抄写有错]
(2sinα-sin2α)/(2sinα+sin2α)
=2sinα(1-cosα)/[2sinα(1+cosα)]
=(1-cosα)/(1+cosα)
=tan² α/2
(2)(1+sin2β)/(sinβ+cosβ)
=(sinβ+cosβ)^2/(sinβ+cosβ)
=sinβ+cosβ.
(3)sinθ(1+cos2θ)
=sinθ*2(cosθ)^2
=(2sinθcosθ)cosθ
=sin2θcosθ.
化简题及证明题请帮帮忙!1.化简:[1-tan²(x+y)]/2tan(x+y)2.证明 ①.(2sinα-s
证明1-tan^2x/1+tan^2x=cos^2x-sin^2x
请问怎么证明sinX+sin(X+Y)+sin(X+2Y)/cosX+cos(X+Y)+cos(X+2Y)=tan(X+
设y=(tan^2 x-csc^2 x )/(tan^2 x+cot^2 x -1) (a)证明y=1- 2/(tan^
证明(1-2sin x cos x )/(cos^2x-sin^2x)=(1-tan x)/(1+tan x)
一道三角恒等式证明题请证明sin(x+y)sin(x-y)=sin^2(x)-sin^2(y)
证明tan^2x-sin^2x=tan^2 sin^2x
已知sin(2α+β)=3sinβ,设tanα=x,tanβ=y,记y=f(x) (1)求证:tan(α+β)=2tan
tan(x+y)tan(x-y)=sin^2x-sin^2y/cos^2x-sin^2y 顺便问一下. tan,sin,
sin(x+y)=1\2,sin(x—y)=1\3,求[tan(x+y)-tanx-tany]\[tany的平方tan(
证明 (tan xsin x)/(tan x-sin x)-(1+cos x)/sin x
已知sin(x+y)=1,求证:tan(2x+3y)=tany