Question

Se stie ca sinx+cosx=$\frac{5}{4}$ . Calculati sin2x

Answer 1

[tex]\sin x + \cos x = \dfrac{5}{4} \Rightarrow (\sin x + \cos x)^2 = \left(\dfrac{5}{4}\right)^2 \\\;\\ \sin^2 x + \cos^2 x +2 \sin x \cos x = \dfrac{25}{16} \\\;\\ 1 +2 \sin x \cos x = \dfrac{25}{16} \Rightarrow 2 \sin x \cos x = \dfrac{25}{16} -1 \\\;\\ \sin2x=\dfrac{9}{16}[/tex]