Question

证明：cos(a+b)*cos(a-b)=cos2b-cos2a

Answer 1

题目错误

当a＝60°,b＝30°时,左边＝0

右边＝cos120°－cos60°＝－1

应改成：2cos(a+b)*cos(a-b)=cos2b+cos2a

右边=cos2b+cos2a

=cos[(a+b)-(a-b)]+cos[(a+b)+(a-b)]

=cos(a+b)cos(a-b)+sin(a+b)sin(a-b)+cos(a+b)cos(a-b)-sin(a+b)sin(a-b)

=2cos(a+b)cos(a-b)