Question

докажите тождество
cos^4x+sin^2x+sin^2x*cos^2x=1

Answer 1

$Cos^{4} x+Sin^{2}x+Sin^{2}x*Cos^{2} x=(Cos^{4} x+Sin^{2}x*Cos^{2} x)+Sin^{2}x=\\\\=Cos^{2} x*\underbrace{(Cos^{2}x+Sin^{2} x)}_{1}+Sin^{2}x=Cos^{2}x+Sin^{2} x=\boxed1$