已知3sina+cosa=0求(1)(3cosa+5sina)/sina-cosa(2)sina+2sinacosa-3cosa
人气:469 ℃ 时间:2020-03-28 03:14:14
解答
sinA 3cosA=2 --->2sin(A/2)cos(A/2) 3[cos(A/2)^2-3(sin(A/2)]^2=2[cos(A/20]^2 [sin(A/2)]^2 --->4[sin(A/2)]^2 2sin(A/2)cos(A/)-2[cos(A/2)]^2=0【两边同除2[cos(A/2)]^2】 --->2[tan(A/2)]^2 tan(A/2)-1=0 --->tan(A/2)=-1或者-1/2.tan(A/2)=-1时,sinA=2tan(A/2)/{1 [tan(A/2]^2}=-1,cosA=0 --->(sinA-cosA)/(sinA cosA)=(-1-0)/(-1 0)=1 tan(A/2)=1/2时,tanA=2tan(A/2)/{1-[tan(A/2)]^2}=4/3 --->(sinA-cosA)/(sinA cosA) =(tanA-1)(tanA 1) =(4/3-1)/(4/3 1) =1/7.
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