[tex]\displaystyle (\sin x+ 7 \cos x)^2+(7 \sin x- \cos x)^2= \\ \\ =\sin^2x+14 \sin x \cos x+49 \cos^2x+49 \sin^2x-14 \sin x \cos x+ \cos^2x= \\ \\ =50 \sin^2x+50 \cos^2x= \\ \\ =50( \sin^2x+\cos^2x)= \\ \\=50. \\ \\ Identitati~folosite: \\ \\ \bullet (a \pm b)^2=a^2 \pm 2ab+b^2 \\ \\ \bullet \sin^2x+\cos^2x=1[/tex]
