Question

cos(a+b)cos(a-b)=1/5,则(cosa)^2-(sinb)^2=?

Answer 1

1/5.

cos(a+b)cos(a-b)=(cosacosb-sinasinb)(cosacosb+sinasinb)

=(cosacosb)^2-(sinasinb)^2

=cosa^2[1-(sinab)^2]-sinb^2[1-(cosa)^2]

=(cosa)^2-(sinb)^2

=1/5