Question

$\frac{{\sin }^{2}A}{{\cos }^{2}A}+\frac{{\cos }^{2}A}{{\sin }^{2}A}={\sec }^{2}Acose{c}^{2}A-2$

Answer 1

$\frac{{\sin }^{2}A}{{\cos }^{2}A}+\frac{{\cos }^{2}A}{{\sin }^{2}A}$

$=\frac{{\sin }^{4}A+{\cos }^{4}A}{{\sin }^{2}A{\cos }^{2}A}$

$=\frac{({\sin }^{2}A+{\cos }^{2}A{)}^2-2{\sin }^{2}A.{\cos }^{2}A}{{\sin }^{2}A{\cos }^{2}A}$

$={\sec }^{2}A.cose{c}^{2}A-2$ [ Since ${\sin }^{2}A+{\cos }^{2}A=1$]