Question

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

• A. $14$
• B. $27$
• C. $23$
• D. $335$

Answer 1

The correct option is C $23$

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