A*cos(x)+j*A*sin(x)=A*exp(j*x) A*cos(x)+j*A*sin(-x)=A*exp(-j*x) If you add the right hand sides of the above equations you get A*exp(j*x)+A*exp(-j*x)=A*cos(x)+j*A*sin(x)+A*cos(x)+j*A*sin(-x) sin(-x)=-sin(x) thus, A*exp(j*x)+A*exp(-j*x)=A*cos(x)+j*A*sin(x)+A*cos(x)-j*A*sin(x) thus A*exp(j*x)+A*exp(-j*x)=A*cos(x)+A*cos(x) thus 2*A*cos(x)=A*exp(j*x)+A*exp(-j*x)