Question

Salut! Fie x un numar real care verifica egalitatea tg x+ctg x=4.Calculati sin 2x.

Answer 1

[tex]\it tgx+ctgx=4 \Leftrightarrow \dfrac{sinx}{cosx} +\dfrac{cosx}{sinx} =4 \Leftrightarrow \dfrac{sin^2x+cos^2x}{sinxcosx} =4 \Leftrightarrow \\\;\\ \\\;\\ \Leftrightarrow \dfrac{1}{sinx cosx} =4 \Leftrightarrow sinx cosx = \dfrac{1}{4}|_{\cdot2}\Leftrightarrow 2sinxcosx=\dfrac{1}{2} \Leftrightarrow sin2x = \dfrac{1}{2}[/tex]