Question

Show that $(1-{\sin }^{2}A)(1+{\tan }^{2}A)=1$

Answer 1

Consider LHS $=(1-{\sin }^{2}A)(1+{\tan }^{2}A)$
$={\cos }^{2}A{\sec }^{2}A$ $[\because 1-{\sin }^{2}A={\cos }^{2}A,1+{\tan }^{2}A={\sec }^{2}A]$
$={\cos }^{2}A\frac{1}{{\cos }^{2}A}=1=$ RHS