Question

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

已知3sinα=-cosα,求1+sinαcosα的值

Answer 1

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.