Question

sin^4x + cos^4x = 0.5

Answer 1

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