Question

证明下列等式成立

(1)cos(x+2/π)=-sinx
(2)sin(π-x)=sinx

Answer 1

证明：
（1）cos(x+2/π)=sin[2/π-(x+2/π)]=sin(-x)=-sinx
（2）sin(π-x)=sin[π-(π-x)]=sinx

Answer 2

cos(x+π/2)=cosxcosπ/2-sinxsinπ/2
=0-1×sinx
=-sinx
sin(π-x)
=sinπcosx-cosπsinx
=0-(-1)×sinx
=sinx