Question

Rezolvati ecuatia: $2(cosx-sinx) = \frac{1}{sinx + cosx}....... x, apartine, [0;\frac{\pi}{2}]$

Answer 1

$2(cosx-sinx)= \frac{1}{sinx+cosx},$, x∈[0; π/2]. Inmultim egalitatea cu sinx+cosx ⇒
$2(cos^2x-sin^2x)=1,sau.cos2x= \frac{1}{2},deci.$ 2x=π/3 ⇒x=π/6.