Question

Aratati ca sin^2(150)+sin^2(60)=1

Answer 1

sin150=sin(pi-30)=sin30=1/2
$(\frac{1}{2}) ^{2}+ (\frac{ \sqrt{3} }{2})^{2} } = \frac{1}{4}+ \frac{3}{4}=1$

Answer 2

Se vor folosi 3 formule:

[tex]1)sin^2x+cos^2x=1\\ 2)sin(x)=sin(180-x)\\ 3)sin(x)=cos(90-x)\\ \\ Din~a~2~formula:\\ \\ sin^2(150)=sin^2(180-150)=sin^2(30)\\ \\ Dupa~care~din~a~3~formula:\\ \\ sin^2(30)=cos^2(90-30)=cos^2(60)\\ \\ Inlocuim:\\ \\ sin^2(150)+sin^2(60)=cos^2(60)+sin^2(60)\\ \\ Din~prima~formula:\\ \\ cos^2(60)+sin^2(60)=1.\\ \\ Ce ~trebuia~ de~ demonstat.[/tex]