Question

3.已知tan=1/3 求(sin+2sin)/(cos+2si

Answer 1

问：3.已知tan=1/3 求(sin+2sin)/(cos+2si

答：您好，亲亲这边为您查询到：∵tanα=1/3∴sinα/cosα=1/3∴cosα=3sinαsin^2α+sinαcosα+2cos^2α=(sin^2α+sinαcosα+2cos^2α)/(sin²α+cos²α)=(sin²α+3sin²α+2*9sin²α)/(sin²α+9sin²α)=22sin²α/(10sin²α)=11/5。

答：相关资料：因为 tan Θ =1/3,所以 cos 2Θ +2 sin 2Θ= [ (cos Θ)^2 -(sin Θ)^2 +4 sin Θ cos Θ ] / [ (sin Θ)^2 +(cos Θ)^2 ]= [ 1 -(tan Θ)^2 +4 tan Θ ] / [ (tan Θ)^2 +1 ]= [ 1 -(1/3)^2 +4 *(1/3) ] / [ (1/3)^2 +1 ]= 2.= = = = = = = = =弦化切.即 除以 [ (sin Θ)^2 +(cos Θ)^2 ] ,然后分子分母同时除以 (cos Θ)^2 .我以前没学万能公式,都是用这种方法.如果你学了万能公式,直接代公式.