1不查表,求2sin20+cos10+tan20sin10的值 2已知向量a=(2,1+sinx),b+(1,cosx),求当x属于[π/4,π/2]时,求a.b的取值范围
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![1不查表,求2sin20+cos10+tan20sin10的值 2已知向量a=(2,1+sinx),b+(1,cosx),求当x属于[π/4,π/2]时,求a.b的取值范围](/uploads/image/z/15177890-2-0.jpg?t=1%E4%B8%8D%E6%9F%A5%E8%A1%A8%2C%E6%B1%822sin20%2Bcos10%2Btan20sin10%E7%9A%84%E5%80%BC+2%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%282%2C1%2Bsinx%29%2Cb%2B%281%2Ccosx%29%2C%E6%B1%82%E5%BD%93x%E5%B1%9E%E4%BA%8E%5B%CF%80%2F4%2C%CF%80%2F2%5D%E6%97%B6%2C%E6%B1%82a.b%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
1不查表,求2sin20+cos10+tan20sin10的值 2已知向量a=(2,1+sinx),b+(1,cosx),求当x属于[π/4,π/2]时,求a.b的取值范围
1不查表,求2sin20+cos10+tan20sin10的值 2已知向量a=(2,1+sinx),b+(1,cosx),求当x属于[π/4,π/2]时,求a.b的取值范围
1不查表,求2sin20+cos10+tan20sin10的值 2已知向量a=(2,1+sinx),b+(1,cosx),求当x属于[π/4,π/2]时,求a.b的取值范围
1.2sin20°+cos10°+tan20sin10°
=2sin20°+cos10°+sin20(sin10°/cos20°)
=2sin20°+[(cos20°cos10°+sin20sin10°)/cos20°]
=2sin20°+[cos(20°-10°)/cos20°]
=2sin20°+(cos10°/cos20°)
=(2sin20°cos20°+cos10°)/cos20°
=(sin40°+cos10°)/cos20°
=(sin40°+sin80°)/cos20°
=2sin[(40°+80°)/2]*cos[(40°-80°)/2]/cos20°
=2sin60°*cos20°/cos20°
=2*√3/2
=√3
2.a*b=(2,1+sinx)*(1,cosx)
=2+(1+sinx)cosx
=2+cosx+sinx*cosx
=2+cosx(1+sinx)
x属于[π/4,π/2]
则cosx(1+sinx)属于[0,(根号2+1)/2]
则a*b=2+cosx(1+sinx)属于
[2,(根号2+5)/2]
1.a=√3
2.[2,(根号2+5)/2]