高一数学急!简单的三角函数sinα+cosα=√2,则sinαcosαsin^4α+ cos^4α=sinα+cosα=1/5(0

arctan1/25 和 arctan25

1、sinα+cosα=√2
(sinα+cosα)^2=2
2sinacosa+1=2
sinacosa=1/2
sin^4α+ cos^4α=(sin^2a+cos^2a)^2-2(sinacosa)^2=1-2*1/4=1/2
2、sinα+cosα=1/5
1+2sinacosa=1/25
2sinacosa=-24/25
(sin-cosα)^2=1-2sinacosa=1+24/25=49/25
sina-cosa=7/5
sinα+cosα=1/5
sina=3/5 cosa=-2/5 tana=-3/2
3、Sinθcosθ=60/169 且π/4(sina+cosa)^2=1+120/169=289/169 sina+cosa=17/13
(sina-cosa)^2=1-120/169=49/169 sina-coa=7/13
sina=12/13
cosa=5/13

1,sinα+cosα=√2
两边平方得1+2sinαcosα=2
sinαcosα=1/2
sin^4α+ cos^4α=(sin^2α+ cos^2α)^2-2sin^2α cos^2α=1-2*1/4=1/2
2.sinα+cosα=1/5 (1)
两边平方得1+2sinαcosα=1/25
2sinαcosα=-24/25
(sinα-cosα)^2=1-2sinαcosα=49/25
sinα-cosα=7/5 (2) sinα-cosα=-7/5(舍去)(因为0