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sin x +cos x= 5/4. calculati sin 2x.

Răspuns :

[tex](sinx+cosx)^{2} = sin^{2}x+2sinxcosx+cos^2x \\ (\frac{5}{4} )^{2} = 1+sin2x \Rightarrow sin2x= \frac{25}{16} -1 \Rightarrow sin2x = \frac{25-16}{16} \Rightarrow \\ \Rightarrow sin2x = \frac{9}{16} [/tex]