(sina+cosa)²+(cosa-sina)²
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(sinA + cosA)² + (sinA - cosA)²
= sin²A + cos²A + 2sinA.cosA + sin²A + cos²A - 2sinA.cosA
= 1 + 2sinA.cosA + 1 - 2sinA.cosA
= 1 + 1
= 2.
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