搜狗做题网求下面三道简单三角函数的题目的解析,谢谢
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求下面三道简单三角函数的题目的解析,谢谢
30 .cotC=cotA+cotB===>cosC/sinC=cosA/sinA+cosB/sinB=(cosAsinB+sinAcosB)/(sinAsinB)=sin(A+B)/(sinAsinB)
=sinC/(sinAsinB)===>cosC=sin^2C/(sinAsinB)=c^2/(ab)=(a^2+b^2-c^2)/(2ab)===>2c^2=a^2+b^2-c^2===>3c^2=a^2+b^2
===>d=3.
29.sin(A-B)/sin(A+B)=-(a+c)/c===>sin(A-B)/sinC=-(sinA+sinC)/sinC===》sin(A-B)+sinA+sinC=0
===>sin(A+B)+sin(A-B)+sinA=0===>2sinAcosB+sinA=0(sinA>0) ===>2cosB+1=0===>B=2PAI/3
27.C+A=PAI-B .(1) C-A=PAI/2.(2) (1)-(2)===>2A=PAI/2-B
所以 cos2A=SINB=1/3===>1-2(sinA)^2=1/3===>sinA=根号3/3.
再问： 好的，告诉我下sin(A-B)==-(sinA+sinC)怎么来的
再答： 根据正弦定理有：-(a+c)/c=-(sinA+sinC)/sinC，===>sin(A-B)/sinC=-(sinA+sinC)/sinC，分母相同，分子必相等。所以 sin(A-B)==-(sinA+sinC)
=sinC/(sinAsinB)===>cosC=sin^2C/(sinAsinB)=c^2/(ab)=(a^2+b^2-c^2)/(2ab)===>2c^2=a^2+b^2-c^2===>3c^2=a^2+b^2
===>d=3.
29.sin(A-B)/sin(A+B)=-(a+c)/c===>sin(A-B)/sinC=-(sinA+sinC)/sinC===》sin(A-B)+sinA+sinC=0
===>sin(A+B)+sin(A-B)+sinA=0===>2sinAcosB+sinA=0(sinA>0) ===>2cosB+1=0===>B=2PAI/3
27.C+A=PAI-B .(1) C-A=PAI/2.(2) (1)-(2)===>2A=PAI/2-B
所以 cos2A=SINB=1/3===>1-2(sinA)^2=1/3===>sinA=根号3/3.
再问： 好的，告诉我下sin(A-B)==-(sinA+sinC)怎么来的
再答： 根据正弦定理有：-(a+c)/c=-(sinA+sinC)/sinC，===>sin(A-B)/sinC=-(sinA+sinC)/sinC，分母相同，分子必相等。所以 sin(A-B)==-(sinA+sinC)