[tex]sec^2x+csc^2x=(sec^2x)(csc^2x)\\\\L=\frac{1}{cos^2x}+\frac{1}{sin^2x}=\frac{sin^2x}{cos^2xsin^2x}+\frac{cos^2x}{cos^2xsin^2x}=\frac{sin^2x+cos^2x}{cos^2xsin^2x}=\frac{1}{cos^2xsin^2x}\\\\=\frac{1}{cos^2x}\cdot\frac{1}{sin^2x}=sec^2x\cdot csc^2x=R[/tex]