求三角函数方程求α,142rad,0.785rad
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  • 2tan α+4=3√2sec α,

    2sin α/cos α+4=3√2/cos α,

    2sin α+4cos α=3√2,得sin α=(3√2-4cos α)/2,代入

    (sin α)^2+(cos α)^2=1,得cos α=7√2/10或cos α=√2/2.

    所以α=arccos(7√2/10)≈8.13度=8.13÷180×3.14≈0.142rad或

    α=arccos(√2/2)=45度=45÷180×3.14=0.785rad.

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