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What is \(\sin^2\left(\frac{\pi}{4}+\theta\right)-\sin^2\left(\frac{\pi}{4}-\theta\right)\) equal to?
Formula used:cos(\(\frac{\pi}{2}-?\)) = sin ? cos2? - sin2? = cos 2? Calculation:Let the required value be y.? y = \(\sin^2\left(\frac{\pi}{4}+?\right)-\sin^2\left(\frac{\pi}{4}-?\right)\)Since cos(\(\frac{\pi}{2}-?\)) = sin ? ? y = \(\cos^2\left(\frac{\pi}{2}-(\frac{\pi}{4}+?)\right)-\sin^2\left(\frac{\pi}{4}-?\right)\)? y = \(\cos^2\left(\frac{\pi}{4}-?\right)-\sin^2\left(\frac{\pi}{4}-?\right)\)We know that, cos2? - sin2? = cos 2? ? y = cos 2(\(\frac{\pi}{4}-?\))? y = cos (\(\frac{\pi}{2}-2?\)) = sin 2? ? \(\sin^2\left(\frac{\pi}{4}+?\right)-\sin^2\left(\frac{\pi}{4}-?\right)\) = sin 2?
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