Question

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Answer 1

Răspuns:

sin 2x = 8/9

Explicație pas cu pas:

sin x + 1/3 = cos x =>

cos x - sin x = 1/3

sin 2x = 2·sin x· cos x

cos² x + sin² x = 1

(cos x - sin x)² = cos²x - 2·sin x ·cos x + sin² x = 1 - 2·sin x ·cos x =

= 1 - sin 2x = (1/3)² = 1/9  =>

sin 2x = 1 - 1/9  = > sin 2x = 8/9

Answer 2

$\it sinx+\dfrac{1}{3}=cosx \Rightarrow sinx-cosx=-\dfrac{1}{3}\Rightarrow (sinx-cosx)^2=\Big(-\dfrac{1}{3}\Big)^2 \Rightarrow\\ \\ \\ \Rightarrow sin^2x-2sinx cosx+cos^2x=\dfrac{1}{9} \Rightarrow 1-\dfrac{1}{9}=2sinxcosx \Rightarrow sin2x =\dfrac{8}{9}$