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The phase function $\cos t$ attains its global maximum $1$ on $[0,3\pi ]$ at the stationary endpoint $t=0$ and at the interior point $t=2\pi$. At either point,By Laplace's method at a nondegenerate stationary endpoint, the endpoint contributesBy Laplace's method, the interior maximum contributesThe remaining parts of the interval are exponentially smaller. Summing the two contributions according to Laplace's method with multiple global maxima gives