【高一】三角函数证明题tan A/2 = sinA/1+cosA = 1-cosA/sinA_数学解答

【高一】三角函数证明题
tan A/2 = sinA/1+cosA = 1-cosA/sinA

人气：352 ℃　时间：2020-05-15 20:32:16

解答

sinA/(1+cosA)
=[2sin(A/2)cos(A/2)]/[1+2cos²(A/2)-1]
=[2sin(A/2)cos(A/2)]/[2cos²(A/2)]
=sin(A/2)/cos(A/2)
=tan(A/2)
(1-cosA)/sinA
={1-[1-2sin²(A/2)]}/[2sin(A/2)cos(A/2)]
=2sin²(A/2)/[2sin(A/2)cos(A/2)]
=sin(A/2)/cos(A/2)
=tan(A/2)