13、化简:(1)3√15sinx+3√5cosx (2)3/2cosx-√3/2sinx (3)√3sinx/2+co
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/15 02:29:37
13、化简:(1)3√15sinx+3√5cosx (2)3/2cosx-√3/2sinx (3)√3sinx/2+cosx/2
(4)√2/4sin(π/4-x)+√6/4cos(π/4-x) (5)sin347°cos148°+sin77°cos58°
(6)sin164°sin224°+sin254°sin314° (7)sin(a+b)cos(γ-b)-cos(b+a)sin(b-γ)
(8)sin(a-b)cos(b-γ)-cos(a-b)sin(γ-b)
(9)tan5π/4+tan5π/12 / 1-tan5π/12
(10)sin(a+b)-2sinacosb) / 2sinasinb+cos(a+b)
(4)√2/4sin(π/4-x)+√6/4cos(π/4-x) (5)sin347°cos148°+sin77°cos58°
(6)sin164°sin224°+sin254°sin314° (7)sin(a+b)cos(γ-b)-cos(b+a)sin(b-γ)
(8)sin(a-b)cos(b-γ)-cos(a-b)sin(γ-b)
(9)tan5π/4+tan5π/12 / 1-tan5π/12
(10)sin(a+b)-2sinacosb) / 2sinasinb+cos(a+b)
1)3√15sinx+3√5cosx
=6√5(√3/2sinx+1/2cosx )
=6√5sin(x+π/3)
2)3/2cosx-√3/2sinx
=√3(√3/2cosx-1/2sinx )
=√3cos(x+π/6)
3)√3sinx/2+cosx/2
=2(√3/2sinx/2+1/2cosx/2 )
=2sin(x/2+π/6)
4)√2/4sin(π/4-x)+√6/4cos(π/4-x)
=√2/2[1/2sin(π/4-x)+√3/2cos(π/4-x) ]
=√2/2sin(5π/12-x)
5)sin347°cos148°+sin77°cos58°
=sin13°cos32°+cos13°sin32°
=sin50°
6)sin164°sin234°+sin254°sin314°(题有误应该是sin234°)
=-sin16°sin54°+sin74°sin46°
=-sin16°sin54°+cos16°cos54°
=cos70°
7)sin(a+b)cos(γ-b)-cos(b+a)sin(b-γ)
=sin(a+b)cos(γ-b)+cos(b+a)sin(γ-b)
=sin(a+b+γ-b)
=sin(a+γ)
8)sin(a-b)cos(b-γ)-cos(a-b)sin(γ-b)
=sin(a-b)cos(γ-b)-cos(a-b)sin(γ-b)
=sin(a-b-γ+b)
=sin(a-γ)
9)tan5π/4+tan5π/12 / 1-tan5π/12
=tanπ/4+tan5π/12 / 1-tan5π/12
=(tanπ/4+tan5π/12) / (1-tanπ/4*tan5π/12 )
=tan(π/4+5π/12)
=tan2π/3
=-√3
10)sin(a+b)-2sinacosb) / 2sinasinb+cos(a+b)
=[sinacosb+cosasinb-2sinacosb]/[cosacosb-sinasinb+ 2sinasinb]
=(cosasinb-sinacosb)/(cosacosb+sinasinb)
=sin(b-a)/cos(b-a)
=tan(b-a)
=6√5(√3/2sinx+1/2cosx )
=6√5sin(x+π/3)
2)3/2cosx-√3/2sinx
=√3(√3/2cosx-1/2sinx )
=√3cos(x+π/6)
3)√3sinx/2+cosx/2
=2(√3/2sinx/2+1/2cosx/2 )
=2sin(x/2+π/6)
4)√2/4sin(π/4-x)+√6/4cos(π/4-x)
=√2/2[1/2sin(π/4-x)+√3/2cos(π/4-x) ]
=√2/2sin(5π/12-x)
5)sin347°cos148°+sin77°cos58°
=sin13°cos32°+cos13°sin32°
=sin50°
6)sin164°sin234°+sin254°sin314°(题有误应该是sin234°)
=-sin16°sin54°+sin74°sin46°
=-sin16°sin54°+cos16°cos54°
=cos70°
7)sin(a+b)cos(γ-b)-cos(b+a)sin(b-γ)
=sin(a+b)cos(γ-b)+cos(b+a)sin(γ-b)
=sin(a+b+γ-b)
=sin(a+γ)
8)sin(a-b)cos(b-γ)-cos(a-b)sin(γ-b)
=sin(a-b)cos(γ-b)-cos(a-b)sin(γ-b)
=sin(a-b-γ+b)
=sin(a-γ)
9)tan5π/4+tan5π/12 / 1-tan5π/12
=tanπ/4+tan5π/12 / 1-tan5π/12
=(tanπ/4+tan5π/12) / (1-tanπ/4*tan5π/12 )
=tan(π/4+5π/12)
=tan2π/3
=-√3
10)sin(a+b)-2sinacosb) / 2sinasinb+cos(a+b)
=[sinacosb+cosasinb-2sinacosb]/[cosacosb-sinasinb+ 2sinasinb]
=(cosasinb-sinacosb)/(cosacosb+sinasinb)
=sin(b-a)/cos(b-a)
=tan(b-a)
13、化简:(1)3√15sinx+3√5cosx (2)3/2cosx-√3/2sinx (3)√3sinx/2+co
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