Question

If $\tan A+\cot A=2,$ then the value of ${\tan }^{10}A+{\cot }^{10}A$ is

• A. $2^{10}$
• B. $1$
  
• C. $2$
• D. $4$

Answer 1

The correct option is C $2$

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

$⟹\tan A+\frac{1}{\tan A}=2$

$⟹\frac{{\tan }^{2}A+1}{\tan A}=2$

$⟹{\tan }^{2}A+1=2\tan A$

$⟹(\tan A{)}^2+(1{)}^2-2\left(\tan A\right)\left(1\right)=0$

$⟹(\tan A-1{)}^2=0$

$⟹\tan A=1⟹\cot A=1$

${\tan }^{10}A+{\cot }^{10}A=1^{10}+1^{10}=2$