Question

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

Answer 1

Given $\tan A+\cot A=2$

Squaring on both sides

$(\tan A+\cot A{)}^2=2^2$

${\tan }^{2}A+{\cot }^{2}A+2\tan A\cot A=‘4$

${\tan }^{2}A+{\cot }^{2}A+2=4$

${\tan }^{2}A+{\cot }^{2}A=2$