Question

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

• A. 2
• B. 1
• C. 4
• D. 5

Answer 1

The Correct Option is A

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