Question

Answer 1

 

(3)[解法一]令 f(x)=sinx+cosx，α=

则g(x)=f(x+α)= sin(x+)+cos(x+)

=cosx-sinx，

于是h(x)= f(x)·f(x+α)

= (sinx+cosx)(cosx-sinx)

=cos2x.

[解法二]令f(x)=1+sinx，α=π，

g(x)=f(x+α)= 1+sin(x+π)

=1-sinx，

于是h(x)= f(x)·f(x+α)

= (1+sinx)( 1-sinx)

=cos2x.