Transforming complex exponentials into sin and cos

The sincos or exp2trig command uses the identity e^{i x}=cos(x)+isin(x) to rewrite complex exponentials in terms of sine and cosine.

sincos(exp(i*x))

cos x+i sin x

exp2trig(exp(-i*x))

cos x−i sin x

simplify(sincos(((i)*(exp((i)*x))^2-i)/(2*exp((i)*x))))

or:

simplify(exp2trig(((i)*(exp((i)*x))^2-i)/(2*exp((i)*x))))

−sin x