Question

若sinα,sinβ是方程x^2—（（√2）cos20°）x+(cos20°)^2—1/2=0的两根,且sinα

Answer 1

sinα+sinβ=√2cos20°

sinα*sinβ=(cos20°)^2—1/2

sin^2α+sin^2β+2sinαsinβ=2(cos20°)^2

sin^2α+sin^2β+2(cos20°)^2-1=2(cos20°)^2

sin^2α+sin^2β=1

只要α+β=90°,sinα