Question

If ${\tan }^4\theta +{\cot }^4\theta =A$, then

• A. $A>2$
• B. $A\ge 2$
• C. $A>4$
• D. $A\ge 4$

Answer 1

The correct option is B $A\ge 2$

${\tan }^4\theta +{\cot }^4\theta =({\tan }^4\theta -{\cot }^4\theta {)}^2+2{\tan }^2\theta {\cot }^2\theta$

$=({\tan }^2\theta -{\cot }^4\theta {)}^2+2$

$\ge 2$ ....(since $({\tan }^2\theta -{\cot }^4\theta {)}^2\ge 0)$