已知3sinα=-cosα,求1+sinαcosα的值(高一数学)急!

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已知3sinα=-cosα,求1+sinαcosα的值(高一数学)急!

已知3sinα=-cosα,求1+sinαcosα的值(高一数学)急!
已知3sinα=-cosα,求1+sinαcosα的值(高一数学)急!

已知3sinα=-cosα,求1+sinαcosα的值(高一数学)急!
3sinα=-cosα
两边取平方,
9(sinα)^2 = (-cosα)^2
9(sinα)^2 = (cosα)^2
两边同时加上(sinα)^2
9(sinα)^2 +(sinα)^2 = (cosα)^2 +(sinα)^2
10(sinα)^2 =1
(sinα)^2 =1/10...(1)
1+sinαcosα...(将3sinα=-cosα带入)
= 1 +sinα*(-3sinα)
= 1 -3(sinα)^2...(将(1)带入)
= 1 -3*1/10
= 7/10.