Find power of a sum of sinusoids
HINT:
For real-valued periodic signal $x$ with period $T_0$ Parseval gives you
$$
P=\frac 1T_0\int_{-T_0/2}^{T_0/2} x^2(t)\mathrm{d}t = \sum_{n=-\infty}^{\infty}\lvert c_n\rvert^2
$$
Where $c_n$'s are Fourier coefficients. You can then use the properties in Equations $(1)$ and $(2)$.
$$
\mathcal F \big\{A\cos\left(2\pi f_0 t + \phi\right)\big\} = \frac A2\big[e^{j\phi}\delta\left(f - f_0\right) + e^{-j\phi}\delta\left(f + f_0\right)\big]\tag{1}
$$
$$
\mathcal F \big\{A\sin\left(2\pi f_0 t + \phi\right)\big\} = j\frac A2\big[e^{-j\phi}\delta\left(f + f_0\right)-e^{j\phi}\delta\left(f - f_0\right)\big]\tag{2}
$$
EDIT:
For Equation $(1)$ for instance, applying Parseval above you have the following:
\begin{align}
P&amp;= \sum_{n=-\infty}^{\infty}\lvert c_n\rvert^2\\
&amp;= \lvert c_{-1}\rvert^2 +  \lvert c_{1}\rvert^2\\
&amp; = \frac{A^2}{4}\cdot 1  + \frac{A^2}{4}\cdot 1\tag{$\lvert e^{\pm j\phi} \rvert = 1$} \\
\end{align}