Evaluate : Sin²A+Cos²A+(SinA-CosA)²
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Given :
sin²A + cos²A + (sinA - cosA) ²
Solution :
(x - y)² = x² + y² - 2xy
Here, x = sinA, y = cosA
⇒ sin²A + cos²A + [ (sinA)² + (cosA)² - 2(sinA)(cosA) ]
⇒ sin²A + cos²A + sin²A + cos²A - 2sinAcosA
⇒ 2sin²A + 2cos²A - 2sinAcosA
⇒ 2 (sin²A + cos²A - sinAcosA)
sin²A + cos²A = 1
⇒ 2 (1 - sinAcosA)