Canceling Non-existent Limits

Calculus Level 1

True or false:

Because both the limits, limxsinx \displaystyle \lim_{x\to\infty} \sin x and limxcosx \displaystyle \lim_{x\to\infty} \cos x does not exist, then the difference of their limits must be equal to 0:

limx(sinxcosx)=0  . \lim_{x\to \infty} ( \sin x - \cos x) = 0 \; .

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