f(x)=cos^2x-sin^2x,则f(2005TT/12)=?

题目

f(x)=cos^2x-sin^2x,则f(2005TT/12)=?
我的数学很烂,是在班里倒数的那些.
f(x)是以5为周期的奇函数,且f(-3)=1,tana=2,f(20sinacosa)=?
2005TT/12=2005 派/12

答案

f(x)=cos^2x-sin^2x=cos2x
f(2005π/12)
=cos2005π/6
=cos(-π/6)
=√3/2
----------------------------
tana=2
=>sina=2/√5;cosa=1/√5
=>sinacosa=2/5
=>f(20sinacosa)=f(8)=f(3)=-f(-3)=-1