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82问答网 > 已知tanθ=2，sin^2θ+cos^2θ=1，是怎么解出sinθ=+-（2√5）⼀5？

已知tanθ=2，sin^2θ+cos^2θ=1，是怎么解出sinθ=+-（2√5）⼀5？

2025-03-29 16:37:44

推荐回答（4个）

回答1：

tanθ=sinθ/cosθ=2
即cosθ=sinθ/2
代入
sin^2θ+cos^2θ=1
5/4*sin^2θ=1
sin^2θ=4/5
sinθ=+-（2√5）/5

回答2：

回答3：

sin/cos=2
cos=sin/2
sin^2+(sin/2)^2=1
sin^2=4/5
sin=+/-2根5/5

回答4：

sinθ/cosθ+1/cosθ=5cosθ=√1-(sinθ)^2得出sinθ=1或者12/13

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