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230问答网 > 已知sin a=4⼀5.且a是第二象限的角，求sin2a.cos2a.tan2a的值。求过程

已知sin a=4⼀5.且a是第二象限的角，求sin2a.cos2a.tan2a的值。求过程

2025-03-30 19:12:50

推荐回答（2个）

回答1：

sin a=4/5.
且a是第二象限的角
cosa=-3/5

sin2a=2sinacosa
=2*(4/5)*(-3/5)
=-24/25

cos2a=2(cosa)^2 -1
=2*(-3/5)^2-1
=-7/25

tan2a
=sin2a/cos2a
=24/7

回答2：

a是第二象限角，则cosa<0，又：
cos²a＋sin²a=1
cos²a＋(4/5)²=1
cos²a=9/25
则：cosa=－3/5
tana=sina/cosa=－4/3
则：
sin2a=2sinacosa=－24/25
cos2a=2cos²a－1=7/25
tan2a=sin2a/cos2a=－24/7

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