Show, by counter-example, that the statement "If cos(a) = cos(b) then sin(a) = sin(b)" is false.

Let a=60 and b=300.

Then cos(a)=cos(60)=0.5 and cos(b)=cos(300)=0.5, therefore cos(a)=cos(b).

Then sin(a)=sin(60)=sqrt(3)/2 and sin(b)=sin(300)=-sqrt(3)/2, therefore sin(a)=sin(b) is incorrect.

Therefore we have a contradiction, and the statement is false.