sin($45^\circ$ + $\theta$) – cos($45^\circ$ – $\theta$) is equal to ______.

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sin($45^\circ$ + $\theta$) – cos($45^\circ$ – $\theta$) is equal to 0. Explanation: sin($45^\circ$ + $\theta$) – cos($45^\circ$ – $\theta$) = cos[$90^\circ$ – ($45^\circ$ + $\theta$)] – cos($45^\circ$ – $\theta$) ...[∵ cos($90^\circ$ – $\theta$) = sin$\theta$] = cos($45^\circ$ – $\theta$) – cos($45^\circ$ – $\theta$) = 0

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