Question

若sinθ和cosθ是关于x的方程x^2-2xsinα+sin^2 β=0的两个根.求证:2cos2α=co

Answer 1

sin^2θ+cos^2θ=1

=（sinθ+cosθ）^2-2sinθcosθ

=(2sinα)^2-2sin^2 β(韦达定理)

=4sin^2α-2sin^2 β=1

所以,4sin^2α=1+2sin^2 β

2-4sin^2α=2-1-2sin^2 β

2cos2α=cos2β