Question

高一数学第六题

Answer 1

字写得不太好看，但希望能够帮到你，最后的结果我算了很多次，发现都得不到分母为177，你确认一下答案，如果不对的话你再追问吧

Answer 2

cosA = 4/5，sinA = 3/5，sin(2A) = 2sinA*cosA = 24/25，cos(2A) = (cosA)^2 - (sinA)^2 = 7/25
tanB = 2，B 是锐角，则 cosB = √5 /5，sinB = 2√5 /5，sin(2B)=4/5，cos(2B) = -3/5
那么，
tan(2C)
=tan[2*(180° - A - B)]
=tan[360° - (2A + 2B)]
=tan(2A+2B)
=sin(2A+2B)/cos(2A+2B)
=[sin(2A)*cos(2B) + cos(2A)*sin(2B)]/[cos(2A)*cos(2B) - sin(2A)*sin(2B)]
=[24/25 * (-3/5) + 7/25 * (4/5)]/[(-3/5)*(5/25) - (24/25)*(4/5)]
=[24*(-3) + 7 * 4]/[-3 * 5 - 24 * 4]
=(-44)/(-111)
=44/111

Answer 3

在三角形中，cosA=4/5 则 tanA=3/4 又tanB=2，则 tan(A+B)=(tanA+tanB)/(1-tanAtanB) =(3/4+2)/(1-3/2) =-11/2 tanC=tan(180-A-B)=-tan(A+B)=11/2 tan2C=2tanC/(1-(tanC)^2) =11/(1-121/4)=-44/117

Answer 4