Question

(SinA + cosA)2

+ (SinA - CosA)2 = 2​

Answer 1

${( \sin(a) + \cos(a) )}^{2} + ( \sin(a) - \cos(a) ) {}^{2} \\ = \sin {}^{2} (a) + \cos {}^{2} (a) + 2 \sin(a) \cos(a) +\sin {}^{2} (a) + \cos {}^{2} (a) - 2 \sin(a) \cos(a) \\ = 1 + 1 = 2$

Here I used the formula that sin²(a)+cos²(a) = 1

also both the 2sin(a)cos(a) gets cancelled

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