[tex]1+tan^2y+ \frac{1}{sin^2y} = \frac{1}{sin^2y*cos^2y} \\
\\(\frac{sin(y)}{cos(y)})^2 + \frac{1}{sin^2y} = \frac{1}{sin^2y*cos^2y} -1=0 \\\\
\frac{sin(y)^2}{cos(y)^2} + \frac{1}{sin^2y} - \frac{1}{sin^2y*cos^2y} = -1 \\\\
\frac{sin(y)^2*sin(y)^2}{sin(y)^2*cos(y)^2} + \frac{cos(y)^2*1}{cos(y)^2*sin(y)^2}- \frac{1}{sin^2y*cos^2y}=-1 \\\\
\frac{sin(y)^4}{sin(y)^2*cos(y)^2} + \frac{cos(y)^2}{sin(y)^2*cos(y)^2} - \frac{1}{sin^2y*cos^2y} =-1\\\\
[tex]\frac{sin(y)^4-(1-cos(y)^2}{sin(y)^2*cos(y)^2} =-1\\\\
\frac{sin(y)^4-sin(y)^2}{sin(y)^2*cos(y)^2}=-1\\\\
\frac{(sin(y)^2-1)*sin(y)^2}{sin(y)^2*cos(y)^2}=-1\\\\
\frac{-(-1sin(y)^2)*sin(y)^2}{sin(y)^2*cos(y)^2}=-1\\\\
\frac{-cos(y)^2*sin(y)^2}{sin(y)^2*cos(y)^2}=-1\\\\
-1=-1
[/tex]
y ∈ R \ {[tex] \frac{k\pi}{2} ,[/tex]K ∈ Z}
