Question

If $\tan \alpha +\cot \alpha =a$ then the value of ${\tan }^4\alpha +{\cot }^4\alpha$ is equal to

• A. $a^4+4a^2+2$
• B. $a^4-4a^2+2$
• C. $a^4-4a^2-2$
• D. $a^4+4a^2-2$

Answer 1

Answer: (B)

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