Question

If $\tan A+\cot A=5$ find the value of ${\tan }^{2}A+{\cot }^{2}A$.

Answer 1

$\tan A+\cot A=5$
Squaring both sides:
${\tan }^{2}A+{\cot }^{2}A+2\tan A\cot A=25$
${\tan }^{2}A+{\cot }^{2}A+2=25$
${\tan }^{2}A+{\cot }^{2}A=23$