Question

已知sinα/2+cosα/2=1/2,求cos2α

紧急！~求过程与正解

Answer 1

sinα/2+cosα/2=1/2
平方得
1+sina=1/4
sina=-3/4
cos2a=(cosa)²-(sina)²=1-2sin²a=1-2x(-3/4)²=-1/8

Answer 2

sinα/2+cosα/2=1/2
(sinα/2+cosα/2)^2=1/4
sin^2a/2+2aina/2cosa/2+cos^2a/2=1/4
1+sina=1/4
可得：sina=-3/4
cos2a=1-2sin^2a
=1-9/8
=-1/8