作业帮三角函数的化简求值证明21.已知sin(a+B)cosa-1/2[sin(2a+B)-cosB]=1/2,0
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![三角函数的化简求值证明21.已知sin(a+B)cosa-1/2[sin(2a+B)-cosB]=1/2,0](/uploads/image/z/3015476-44-6.jpg?t=%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0%E7%9A%84%E5%8C%96%E7%AE%80%E6%B1%82%E5%80%BC%E8%AF%81%E6%98%8E21.%E5%B7%B2%E7%9F%A5sin%28a%2BB%29cosa-1%2F2%5Bsin%282a%2BB%29-cosB%5D%3D1%2F2%2C0)
三角函数的化简求值证明21.已知sin(a+B)cosa-1/2[sin(2a+B)-cosB]=1/2,0
三角函数的化简求值证明2
1.已知sin(a+B)cosa-1/2[sin(2a+B)-cosB]=1/2,0
三角函数的化简求值证明21.已知sin(a+B)cosa-1/2[sin(2a+B)-cosB]=1/2,0
1.
sin(2a+B)-cosB=sin[(a+B)+a]-cos[(a+B)-a]
=sin(a+B)cosa+cos(a+B)sina-cosB
所以:
sin(a+B)cosa-1/2[sin(2a+B)-cosB]
=sin(a+B)cosa-1/2sin(a+B)cosa-1/2cos(a+B)sina+1/2cosB
=1/2[sin(a+B)cosa-cos(a+B)sina]+1/2cosB
=1/2(sin(a+B-a)+cosB)
=1/2(sinB+cosB)
=1/2
就是有:sinB+cosB=1
平方一下,就得到sinBcosB=0
又0
也就是B=90度
2.
sin3a=sin(2a+a)=sin2acosa+cos2asina
=2(cosa)^2sina+[1-2(sina)^2]sina
=2sina-2(sina)^3+sina-2(sina)^3
=3sina-4(sina)^3
所以
(sin3a)/sina=13/5=3-4(sina)^2
得到:
(sina)^2=1/10
a为第四象限的角,那么sina=-1/根号10
tana=-1/3
那么就有:
tan2a=2tana/[1-(tana)^2]
=(-2/3)/[1-(1/9)]
=(-2/3)*(9/8)
=-3/4
令a+B 为x 则B为x-a
sinxcosa-1/2[sin(x+a)-cosB]=1/2
2sinxcosa-sin(x+a)+cosB=1
sinxcosa-sinacosx+cosB=1
sin(x-a)+cosB=1
sinB+cosB=1
所以 B=π/2