Question

Să se rezolve ecuatia :
sinx+cosx=
$\sqrt{2}$
tgx=? ​

Answer 1

Sper ca te-am ajutat!Succes!

Answer 2

$sin(x)+cos(x)=\sqrt2\ \Bigr|^2$

$sin^2(x)+2sin(x)cos(x)+cos^2(x)=2$

$1+sin(2x)=2$

$sin(2x)=1$

$2x=2n\pi+\cfrac{\pi}{2},\ n\in\mathbb{Z}$

$x=n\pi+\cfrac{\pi}{4},\ n\in\mathbb{Z}$

Dar $x\in(0,\ \cfrac{\pi}{2})$

Deci singura solutie este atunci cand $n=0$ si anume

${x=\cfrac{\pi}{4}$

Deci

$\boxed{tg(x)=tg\left(\cfrac{\pi}{4}\right)=1}$