求高手解答三角函数式..全部求出者追加50分,谁多采纳谁的,1.tana-cota=1.,则tan³a-cot³a等于多少?2.（1+cos2分之1）/（1-cos2分之1）等于多少?3.已知sina=5分之根号5,则（cosa+sina）分之（cosa-sina

Question

求高手解答三角函数式..全部求出者追加50分,谁多采纳谁的,
1.tana-cota=1.,则tan³a-cot³a等于多少?
2.（1+cos2分之1）/（1-cos2分之1）等于多少?
3.已知sina=5分之根号5,则（cosa+sina）分之（cosa-sina）+（cosa-sina）分之（cosa+sina）等于多少?
4.tan15°+cot15°等于多少?
5.已知（2cosx-sinx）（sinx+cosx-3）=0,则sec²x等于多少?
6.sin40°*（tan10°- 根号3）等于多少?
7.cos9分之π*cos9分之2π*cos9分之3π*cos9分之4π等于多少?
8.已知sina=4/5,2分之π〈a〈π ,则tana等于多少?
9.若a食第二象限角,且根号（1+sin2分之a）=cos2分之a+sin2分之a,那么2分之a是第几象限?
10.sin1/1- cos1等于多少?
11.已知sin四次方a+cos四次方a=5/9,π小于a小于2分之3π,则tana+cota等于多少?
12.已知a=5分之39π,则sina和cosa分别比0大或小?

Answer 1

1、
x=tana,y=cota
=>
(x-y)^2=1
=>
x^2+y^2-2xy=1
=>
x^2+y^2=1+2=3
x^3-y^3=(x-y)(x^2+y^2+xy)
=>
原式
=x^2+y^2+xy
=x^2+y^2+1
=3+1
=4
2、
cos0.5=2cos20.25-1=1-2sin20.25
=>
1+cos0.5=2cos20.25
1-cos0.5=2sin20.25
=>
(1+cos0.5)/(1-cos0.5)
=2cos20.25/(2sin20.25)
=(cos0.25/sin0.25)^2
=ctg20.25
3、
原式
=(cosa-sina)/(cosa+sina)+(cosa+sina)/(cosa-sina)
=((cosa-sina)^2+(sina+cosa)^2)/((cosa+sina)(cosa-sina))
=2/(cos2a-sin2a)
=2/(1-2sin2a)
=2/(1-2*(√5/5)2)
=2/(1-2/5)
=10/3
4、
tan15+cot15
=sin15/cos15 + cos15/sin15
= (sin215+cos215)/(sin15cos15)
= 1/sin15cos15
=2/sin30
=4
5、
（2cosx-sinx）（sinx+cosx-3）=0
sinx+cosx≤√2
=>
sinx+cosx≠0
=>
2cosx-sinx=0
=>
tanx=2
=>
sec2x
=1+tan2x
=5
6、
sin40°*（tan10°- 根号3）
=sin40(tan10-tan60)
=sin40*tan(10-60)*(1+tan10tan60)
=-cos50tan50(cos10cos60+sin10sin60)/(cos10cos60)
=-sin50cos(10-60)/(cos10sin30)
=-2sin50cos50/cos10
=-sin100/cos10
=-sin80/cos10
=-1
7、
cos(pi/9)cos(2pi/9)cos(3pi/9)cos(4pi/9)
=cos20cos40cos60cos80
=cos20cos40cos60sin10
=sin10cos10cos20cos40cos60/cos10
=sin10cos10cos20cos40/2cos10
=sin20cos20cos40/4cos10
=sin40cos40/8cos10
=sin80/16cos10
=1/16
8、
sina=4/5
=>
cosa=±3/5
第二象限
=>
cosa=-3/5
=>
tana
=sina/cosa
=(4/5)/(-3/5)
=-4/3
9、
根号（1+sin2分之a）=cos2分之a+sin2分之a
=>
1+sin(a/2)=(cos(a/2)+sin(a/2))2
=>
1+sin(a/2)=1+2cos(a/2)sin(a/2)
=>
1+sin(a/2)=1+sina
=>
sin(a/2) = sina
=>
sin(a/2)=2sin(a/2)cos(a/2)
=>
cos(a/2)=0.5
=>
a/2=±60+k*360
=>
a=±120+k*720
第二象限
=>
a=120+k*720
=>
a/2=60+k*360
=>
第一象限
10、
sin1/(1-cos1)
=2sin0.5cos0.5/2sin0.5sin0.5
=cos0.5/sin0.5
=cot0.5
11、
sin?a+cos?a=5/9
=>
(sin2a+cos2a)2-2sin2acos2a=5/9
=>
2sin2acos2a=4/9
=>
sinacosa=±√2/3
π小于a小于2分之3π
=>
sina0
=>
sinacosa=√2/3
=>
tana+cota
=sina/cosa+cosa/sina
=(sin2a+cos2a)/sinacosa
=1/(√2/3)
=3/√2
12、
sin(39pi/5)
=sin(39pi/5-2pi*4)
=sin(-pi/5)
=-sin360