Question

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

Answer 1

Given tan A + cot A = 2
$\therefore (tanA+\cot A{)}^2=4$
$\Rightarrow ta{n}^{2}A+{\cot }^{2}A+2tanAcotA=4$
$\Rightarrow ta{n}^{2}A+{\cot }^2=4-2$ $[tanA=\frac{1}{\cot A}]$
$\Rightarrow ta{n}^{2}A+co{t}^{2}A=2$