Question

1)Aratati ca sin^2 135° + sin^2 45° =1
2) Se stie ca cosx= 0,7 => cos(x+pi) =?​

Answer 1

 

$\displaystyle\bf\\1)\\\\sin\,135^o=sin(180^o-45^o)=sin\,45^o\\\\sin^2135^o+sin^245^o=sin^245^o+sin^245^o===\\\\=\left(\frac{\sqrt{2}}{2}\right)^2+\left(\frac{\sqrt{2}}{2}\right)^2=\\\\\\=\frac{2}{4}+\frac{2}{4}=\frac{2+2}{4}=\frac{4}{4}=\boxed{\bf1}\\\\\implies~\boxed{\bf~sin^2135^o+sin^245^o=1}$

.

$\displaystyle\bf\\2)\\\\cos\,x=0,7\\0,7>0\\\implies~x~~este~in~cadranul~1~sau~cadranul~4.\\x+\pi=x+180^o~este~in~cadranul~2~sau~in~cadranul~3.\\In~cadranele~2~si~3~cosinusul~este~negativ.\\Le~aducem~la~cadranul~1.\\Din~cadranul~2~avem:\\cos(180-x)=-cos\,x=-0,7\\Din~cadranul~3~avem:\\cos(180+x)=-cos\,x=-0,7\\\\\implies~~\boxed{\bf~cos(x+\pi)=-cos\,x=-0,7}$