Question

sin^4x + cos^4x = 0.5

Answer 1

$Sin^{4}x+Cos^{4}x=0,5\\(Sin^{2}x+Cos^{2} x)^{2}-2SinxCosx=0,5\\1-Sin2x=0,5\\Sin2x=frac{1}{2}\\2x=(-1)^{n}arcSinfrac{1}{2}+pi n,nez\\2x=(-1)^{n}frac{pi }{6}+pi n,nez\\x=(-1)^{n} frac{pi }{12}+frac{pi n }{2},nez$