Question

If $|tanA+\cot A=2$, then the value of ${\tan }^{4}A+{\cot }^{4}A=$

• A. 2
• B. 1
• C. 4
• D. 5

Answer 1

Answer: (A)

$\tan A+\cot A=2$
$\Rightarrow (\tan A+\cot A{)}^2=4$
$\Rightarrow {\tan }^{2}A+{\cot }^{2}A+2\tan A\cot A=4$
$\Rightarrow {\tan }^{2}A+{\cot }^{2}A=2$
$\Rightarrow {\left({\tan }^{2}A+{\cot }^{2}A\right)}^2=4$
$\Rightarrow {\tan }^{4}A+{\cot }^{4}A+2{\tan }^{2}A{\cot }^{2}A=4$
$\Rightarrow {\tan }^{4}A+{\cot }^{4}A=2$