Question

Verify the following equalities.
$1+{\tan }^2{45}^{\circ }={\sec }^2{45}^{\circ }$

Answer 1

$1+{\tan }^{2}45°={\sec }^{2}45°$

$\Rightarrow L.H.S=1+{\tan }^{2}45°=1+1=2$

$\Rightarrow R.H.S={\sec }^{2}45°={\left(\sqrt{2}\right)}^2=2$

$\therefore L.H.S=R.H.S$

Hence, the answer is verify.