Question

sinx +3cos x=2 radical 2 stiind ca tgx=1, x apartine (0,pi/2)​

Answer 1

Explicație pas cu pas:

$Cum~x~\in~(0,\frac{\pi}{2})~si~tg~x=1, x=\frac{\pi}{4}~pentru~ca~tangenta~\frac{\pi}{4}=1.$

$Inlocuim~x~cu~\frac{\pi}{4}.$

$Stim~ca~sin\frac{\pi}{4}=\frac{\sqrt2}{2} =cos\frac{\pi}{4}$

$\frac{\sqrt2}{2}+3* \frac{\sqrt2}{2}=\frac{4\sqrt2}{2}=2\sqrt2$

Answer 2

$\it x\in\Big(0,\ \dfrac{\pi}{2}\Big),\ \ tgx=1 \Rightarrow x=\dfrac{\pi}{4}\\ \\ \\ sin\dfrac{\pi}{4} + 3cos\dfrac{\pi}{4} = \dfrac{\sqrt2}{2}+3\cdot\dfrac{\sqrt2}{2}=\dfrac{\sqrt2+3\sqrt2}{2}=\dfrac{4\sqrt2}{2}=2\sqrt2$