Question

If $\sin A=\cos A$, find the value of
$2{\tan }^{2}A-2{\sec }^{2}A+5$

Answer 1

Given, $\sin A=\cos A$
$\tan A=1$
$\tan A=\tan 45$
$A={45}^{\circ }$
Now, $2{\tan }^{2}A-2{\sec }^{2}A+5$
= $2{\tan }^{2}45-2{\sec }^{2}45+5$
= $2(1{)}^2-2(\sqrt{2}{)}^2+5$
= $2-4+5$
= $3$