Question

1+cos(x^2+1)=sin^2(x^2+1)

Answer 1

$1+cos(x^2+1)=sin^2(x^2+1)\\x^2+1=t\\1+cos(t)=sin^2(t)\\1+cos(t)=1-cos^2(t)\\cos^2(t)+cos(t)=0\\cos(t)(cos(t)+1)=0\\cos(t)=0\\t= \frac{\pi}{2}+\pi k\\x^2+1=\frac{\pi}{2}+\pi k\\x^2=\frac{\pi-2}{2} +\pi k\\x=+- \sqrt{\frac{\pi-2}{2}+\pi k } \\cos(t)=-1\\t=\pi +2\pik\\x^2+1=\pi +2\pi k\\x^2=\pi-2\pi k\\x=+- \sqrt{\pi-1+2\pi k}$