Question

sa se transforme in produs:
sinx + cosx

Answer 1

$Avem,sin \alpha +sin \beta =2sin \frac{ \alpha + \beta }{2}cos \frac{ \alpha - \beta }{2}$, deci: sinx+cosx=sinx+sin(π/2-x)=
$2$$sin \frac{x + \frac{ \pi }{2} -x}{2}*cos \frac{x- \frac{ \pi }{2}+x }{2}$=
2$sin \frac{ \pi }{4}*cos(x- \frac{ \pi }{4})=2* \frac{ \sqrt{2} }{2}*cos(x- \frac{ \pi }{4})= \sqrt{2}cos(x- \frac{ \pi }{4})$. Metoda a doua: dam factor fortat pe √2, si avem:
$sinx+cosx=$$\sqrt{2}($$\frac{ \sqrt{2} }{2}cosx+ \frac{ \sqrt{2} }{2}sinx)= \sqrt{2}(cosxcos \frac{ \pi }{4} +sinxsin \frac{ \pi }{4})= \sqrt{2}cos(x- \frac{ \pi }{4})$