If $$\cos\theta + \sin\theta = \sqrt{2}\cos\theta$$, then $$\cos\theta - \sin\theta$$ is
$$\sin^2 \theta + \cos^2 \theta = 1$$
So, $$\sin^2 \theta + \cos^2 \theta + 2\sin\theta * \cos \theta = 2 \cos^2\theta$$
Hence, $$\cos^2 \theta - \sin^2 \theta = 2 \sin\theta*\cos\theta$$
So, $$\cos\theta - \sin\theta = \sqrt{2}\sin\theta$$
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