Question

Prove the given equation​

Answer 1

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$\bold{ (sin \theta + cos \theta) {}^{2} - (sin \theta - cos \theta) {}^{2} } \\ \\ \bold{ =[ (sin \theta) {}^{2} + 2 \: sin \theta \: cos \theta + (cos \theta) {}^{2} ]} \\ \bold{ - [(sin \theta) {}^{2} - 2 \: sin \theta \: cos \theta + (cos \theta) {}^{2}] } \\ \\ \bold{ = (sin {}^{2} \theta+ 2 \: sin \theta \: cos \theta + cos {}^{2} \theta) } \\ \bold{ - (sin {}^{2} \theta - 2 \: sin \theta \: cos \theta +cos {}^{2} \theta)} \\ \\ \bold{ = \cancel{sin {}^{2} \theta} \: + 2 \: sin \theta \: cos \theta + \cancel{cos {}^{2} \theta}} \\ \bold{ - \: \cancel{sin {}^{2} \theta} \: + 2 \: sin \theta \: cos \theta - \cancel{cos {}^{2} \theta}} \\ \\ \bold {= 2 \: sin \theta \: cos \theta + 2\: sin \theta \: cos \theta} \\ \\ \bold{ =4 \: sin \theta \: cos \theta }$

Answer 2

Answer:

Step-by-step explanation: