Question

prove that [tex] (sinx+ cosx)^{2}+(sinx- cosx)^{2}=2
[/tex]

Answer 1

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Answer 2

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