Trigonometric Sums - URSS Calculate the value of the sums:
(a) $\cos x+\binom{n}{1}\cos 2x +\cdots+\binom{n}{n} \cos (n+1)x $;
(b) $\sin x+\binom{n}{1}\sin 2x +\cdots+\binom{n}{n} \sin (n+1)x $.

Hint: Consider the real and imaginary parts of the binomial expansion of $e^{ix}(1+e^{ix})^n$
Then write $$1+e^{ix} = 2e^{ix/2}\cos\frac{x}{2}$$
