(a) Use the reduction formula $$\int {\cos^n(x)}\, dx = \frac{1}{n}\cos^{n-1}(x)\sin(x)+\frac{n-1}{n}\int {\cos^{n-2}(x)}\, dx$$ to evaluate the integral $$\int {\cos^2(x)}\, dx.$$

Note: Use an upper-case "C" for the constant of integration.

(b) Use the reduction formula given above and part(a) to evaluate the integral $$\int {\cos^4(x)}\, dx.$$

Note: Use an upper-case "C" for the constant of integration.