The teacher wants four solutions to the ninth question, that is, the great god solution and the online solution. , four questions reward.

1) let sinα=x and cosα=y, then x+y=2/3.

(x+y)^2=x^2+y^2+2xy

2xy=4/9- 1=-5/9, which means xy=-5/ 18.

Using Vieta's theorem, we know that X and Y are the solutions of the equation P 2-2/3P-5/ 18 = 0, x=(2+√ 14)/6, and y=(2-√ 14)/6.

2) From sinα+cosα=2/3, we get √2sin(α+π/4)=2/3, that is, sin(α+π/4)=√2/3.

By 0

3) Substitute sin α =+-√ [1-(sin α) 2] into sinα+cosα=2/3 to solve the equation.

I really can't think of a fourth method.