Question

Fie x apartine R, astfel incat sinx= 1 supra 2 + cos x. Calculati sin 2x

Answer 1

Stim ca
$\sin{(2x)}=2\sin{x}*\cos{x}$
Atunci din relatia de mai sus
$\sin{x}=\frac{1}{2}+\cos{x}\Rightarrow \sin{x}-\cos{x}=\frac{1}{2}\Rightarrow (\sin{x}-\cos{x})^{2}=\frac{1}{4}\Rightarrow \sin^{2}{x}+\cos^{2}{x}-2\sin{x}\cos{x}=1-\sin{(2x)}=\frac{1}{4}\Rightarrow \sin{2x}=1-\frac{1}{4}=\frac{3}{4}$