f(x)=2sin(2x+π/3)在ΔABC中,若f(c)=√3,2sinB=cos(A-C)-cos(A+C),求tanA的值
问题描述:
f(x)=2sin(2x+π/3)在ΔABC中,若f(c)=√3,2sinB=cos(A-C)-cos(A+C),求tanA的值
答
cos(A-C)-cos(A+C),cosAcosC+sinAsinC-(cosAcosC-sinAsinC)=2sinAsinC=2sinB所以sinAsinC=sinBf(C)=2sin(2C+π/3)=√3所以sin(2C+π/3)=√3/2即2C+π/3=60°或120°当2C+π/3=60°,C=0不符舍去所以2C+π/3=120°,C...